What is the gradient of a line?
the slope, the steepness
How do a lot of people think about the gradient (the slope)?
rise/run... or change in y / change in x
What is a solution to an equation?
A solution is the set of values that makes an equation TRUE.
What does is mean to "satisfy" an equation?
Make the equation true.
When you graph a line, what are you actually graphing?
THE SOLUTION! Those are all of the points that make the equation true. All of the points that "work". If you put any other points, (x,y) into the equation, they won't work, You will get a false statement.
What are the gradients of the diagonals of a square?
+1 going up L to R, and -1 going down from L to R
How can you think of a slope of 1 or -1?
A perfect diagonal of a square, 45 degrees!
What is an interesting fact about slopes between -1 and +1?
HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1
(and they are perpendicular to eachother)
WHat is the gradient of a flat surface?
What is the gradient of a horizontal line?
What is the gradient of a vertical line?
what is the slope of a line that goes straight up and down?
the number 0/5 is equal to :
the number 5/0 is equal to :
Why can't you divide by zero? (why can zero be in the top and not the bottom?)
It doesn't make sense when you think deeply about what division asks. Example: 10/2 asks "how many times do you add 2 to itself to get to 10?" the answer is 5. 10/0 asks "how many times do you add 0 to istelf to get to 10?" the answer is there is no answer. undefined 0/2 asks "how many times do you add 2 to itself to get to 0?" the answer is zero. you add none of them and get zero. 0/0 asks "how many times do you add 0 to itself to get 0?" the answer is 0, or 1, or 2, or any number, so also, undefined.
What is the x intercept of a line? (what are the coordinates?)
Where the line crosses the horizontal axis, the x-axis. The coordinates are ( X, 0 )
What is the y intercept of a line? (what are the coordinates?)
Where the line crosses the vertical axis, the y-axis. The coordinates are ( 0, Y )
How can you find the x intercepts from an equation of a line?
Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)
How can you find the y intercepts from an equation of a line?
Plug zero in for X and solve for Y. he coordinates wll be (0, Y)
what are the coordinates of a point?
(x,y) the x and y value.
What is the y coordinate for all x-intercepts?
zero. all x-intercepts have a height of zero because they are on the x-axis.
What is the x coordinate for all y-intercepts?
zero. All y-intercepts are in the middle, not left or right because they are on the y-axis.
Parallel lines have ______ gradients, or slopes
Perpendicular lines have _____ gradients, or slopes
OPPOSITE SIGN and the RECIPROCAL
If a line has a slope of 2/3 then any line parallel to it will have a slope of ____ and any line perpendicular will have a slope of ___
+2/3 and perp would be -3/2
If a line has a slope of -5, then any line parallel to it will have a slope of __ and any line perpendicular to it will have a slope of ___-
-5 and perp would be +1/5
What is the gradient formula? (the slope formula?)
m = ( y - y ) / ( x - x )
The three forms of equations of a line we use are :
point-gradient form, gradient-intercept form, general form
Why is it called "point-gradient" form?
There is a point and a gradient explicitly shown in the form
what is point-gradient form?
A rearrangement of the gradient formula: y-y =m (x-x)