How do you show that a point lies on a line?

Show that, when you plug coordinates in for x and y in the function, you get a true mathematical statement.

What happens if you plug the coordinates of point (x,y) that is NOT on the line in for x and y in a function?

It will make a FALSE statement

How do you know if a graph will go through the origin?

If you can plug in the coordinates (0,0) in for x and y and get a true statement.

What does it mean to “SOLVE” an equation?

Find values that make the equation true

The graph of an equation is the set of all of the points, (x,y) that _____

will make the equation true when plugged in

what does a slope of zero look like?

horizontal, flat from left to right. The x axis has a slope of zero.

what does a slope that is undefined look like?

vertical, straight up and down. The y axis has a slope of zero.

how can you think of the points on the line y=x to help you graph it?

all of the x values are equal to all of the y values.. so (2,2), (3,3), (5,5), (-100,-100) are all in the solution set and on the line

How can you think of the points on the line y=-x to help you graph it?

the x values are opposite the y values… so (2, -2) and (-2, 2) and (-107, 107).

How can you think of points on the lone y=5 to help you graph it?

all of the points on the cartesian plane with a y value of 5… (2,5), (9,5), (-200,5)

How can you think of the line x=6 to help you graph it?

all of the points on the cartesian plane with an x value of 6: (6, 0), (6, -3), (6, 24.3), (6, -2000)

Describe what the line y=x looks line

positive diagonal line from bottom left to upper right, slope of 1, through the origin

Describe what the line y=-x looks like

negative diagonal line from top left to bottom right, slope of -1, through the origin

describe what the line y=12 looks like

horizontal, from left to right, through (0,12)

describe what the line x=-8 looks like

vertical, straight up and down, through the point (-8,0) on the x axis. undefined slope

what is the origin?

the point (0,0)

what does an undefined slope look like?

up and down (vert)

what does a zero slope look like?

left to right (horiz)

what is the point (0,0) called?

the origin

what is the XY axis graph thing we plot lines and points on called?

the cartesian plane

how can you think of the points on the line y=x to help you graph it?

the x and y are equal. so (2,2), (3,3), (5,5), (-100,-100) are all in the solution set and on the line

How can you think of the points on the line y=-x to help you graph it?

the x and y are opposites. so (2, -2) and (-2, 2) and (-107, 107).

How can you think of points on the line y=5 to help you graph it?

all of the points on the cartesian plane with a y value of 5. (2,5), (9,5), (-200,5)

How can you think of the line x=6 to help you graph it?

all of the points on the cartesian plane with an x value of 6: (6, 0), (6, -3), (6, 24.3), (6, -2000)

How do we write equation of horizontal lines?

y=___

How do we write equations of vertical lines?

x= ____

How do you quickly graph slope intercept form?

plot the given y intercept (0,b) and label, then use the slope to sketch a line through it.

How do you quickly graph point slope form?

plot the given point (x,y) and label, then use the slope to sketch a line through it. Remember the OPPOSITES

How do you quickly graph when in standard linear form?

Find the zeros. Cover the x term to find y intercept (0,y), cover the y term to find the x intercept (x,0).

How would you graph

y= 1/2x + 7

plot (0,7) and sketch a line with a slope of 1/2 through it

How would you graph

y-10=2(x+4)

plot (-4, 10) and sketch a line with a slope of 2 through it

How woudl you graph

2x+5y=20

cover 2x to find that y-int is 4 (0,4), cover the 5y to find that x-int is (10,0)

y= 1/3x -5

What form and what is the y-intercept?

this equation is in slope-intercept form and the y intercept is (0, -5)

y= 1/3x -5

Name the form and name a point on the line

This is equation is in slope intercept form and a point is (0, -5)

y= 1/3x -5

Name the form and find the slope.

This is equation is in slope intercept form and the slope is 1/3

3x+4y=24

Name the form and name a point on the line

This is equation is in standard form and a point is (0, 6) or (8, 0)

3x+4y=24

Name the form and the Y intercept:

This is equation is in standard form and the y intercept is (0, 6). You plug zero in for x and solve for y.

3x+4y=24 Name the form and the X intercept:

This is equation is in standard form and the x intercept is (8,0). Plug zero in for y and solve for x.

y-5=3(x+2)

Name the form and name a point on the line

This is equation is in point slope form and a point is ( -2, 5)

y-5=3(x+2)

Name the form and find the slope.

This is equation is in point slope form and the slope is 3

y-5=3(x+2)

Is the origin (0,0) on this line?

How do you know?

This is equation is in point slope form and if you plug (0,0) in you get -5= 3(2) which is not true, so the origin is not on the line. It is not a solution.

y+7=1/3 (x-10)

Name the form and name a point on the line

This is equation is in point slope form and a point is (10, -7).

y+7=1/3 (x-10)

Name the form and find the slope.

This is equation is in point slope form and the slope is 1/3

y+5=1/2 (x+10)

Is the origin on this line?

How do you know?

This is equation is in point slope form and to check to see if the origin is on the line, you have to see if it is a solution. Plugging in (0,0) for x and y gives 5 = 1/2 (10) which is true, since (0,0) is a solution, It is indeed on the line.

y= 1/2 x

What form and what is the y-intercept?

This is equation is in slope intercept form [y = 1/2x + 0] nd the y intercept is (0,0), the origin

y= 1/2 x

Name the form and find the slope.

This is equation is in slope intercept form and the slope is 1/2.

y= 1/2 x

Is the origin on this line? How do you know?

This is equation is in slope intercept form form and if you plug in (0,0) for (x,y) you get 0=1/2(0) which is true. The line goes through the origin.

y= 1/2 x

Find the y coordinate for this point on the line: (10, ___)

Plug in 10 for x to get y= 1/2 (10) and you get y=5. The point (10, 5) is on the line

x - y = 10 Name the form and name a point on the line.

This is equation is in Standard form and the point (0, -10) or (10, 0) is on the line. You can also pick any (x,y) such that the x is 10 more than the y, so (50, 40) works.

x - y = 10

Name the form and find the y intercept.

This is equation is in standard form and plug 0 in for x to solve for y. (0, -10)

x - y = 10

Name the form and find the x intercept.

This is equation is in standard form and plug 0 in for y and then solve for x. (10, 0)

y+3 = -2(x-8)

Name the form and name a point on the line

This is equation is in point slope form and a point on the line is (8,-3)

y+3 = -2(x-8)

Name the form and find the slope.

This is equation is in point slope form and the slope is -2

y=x NAME 3 POINTS ON THE LINE

all points where x and y are equal. (5, 5), (0,0), (-2,-2)

x=5

NAME 3 POINTS ON THE LINE

all points where x value is 5. (5,8), (5,0), (5,10000)

y= -3 NAME 3 POINTS ON THE LINE

all points where y value is -3. (6,-3), (45, -3), (0, -3),

y=-x NAME 3 POINTS ON THE LINE

all points where x and y are opposites. (5, -5), (-22, 22), (0,0), (48, -48)

y= x

What is the slope?

1

y = -x What is the slope?

-1

y = 4

What is the slope?

0

x = -3 What is the slope?

undefined

x = 0 What is the slope?

undefined

y = 0

What is the slope?

0

x = 0

What special line is this?

this is the equation of the Y axis. All of the points have an x value of zero. Vertical line through (0,0) with undefined slope.

y = 0

What special line is this?

This is the equation of the X axis. All of the points that have a y value of zero. A horizontal line through (0,0) with a slope of zero.

x = 0 name 3 points on the line

any points with an x of zero (0, 6), (0, -9), (0, 0) These are all on the y axis.

y = 0 name 3 points on the line

any points with a y coordinate of zero (9,0), (-300, 0), (0, 0) these are all on the x axis.

Parallel lines have ______ slopes

the same

Perpendicular lines have _____ slopes

OPPOSITE SIGN AND RECIPROCAL: change sign and flip it!!

If one line has a slope of 2/3 and an other line has a slope of 2/3 then we can say these lines are ______

parallel

If one line has a slope of -2/5 and the other has a slope of 2/5, then the lines are _____

perpendicular

what are lines called that go in the same direction?

parallel

what are lines called that cross eachoter at 90 degrees (right angle?)

perpendicular

If a line as a slope of 2/3, then any line parallel to it will have a slope of __

2/3

If a line as a slope of -5, then any line parallel to it will have a slope of ___

-5

If a line has a slope of zero, all parallel lines will have a slope of ___

zero

If a line has a slope of zero, all perpendicular lines will have a slope of ___

undefined

If a line has a slope that is undefined, all parallel lines will have a slope of ___

undefined

If a line has a slope that is undefined, all perpendicular lines will have a slope of ___

zero

If a line has a slope of 3/5 , then any line perpendicular to it will have a slope of ____

5/3

If a line has a slope of -3, then any line perpendicular to it will have a slope of ___.

1/3

If you are given two points and need to find the equation of a line, how do you do it?

First, find the slope using m=(y-y)/(x-x), then use that slope and EITHER OF THE POINTS. Put it in point slope form.

What is the equation of a vertical line passing through (6,5)?

x=6

What is the equation of a horizontal line passing through (6, 5)?

y = 5

What is the equation of the vertical line passing through (-8, 12.6) ?

x = -8

What is the equation of the horizontal line passing through (-8, 12.6)

y = 12.6