What does "gradient" or "slope" describe in normal English words?

It describes how steep or slanty a line is.

What is a "coordinate" or "coordinate pair"?

It's two numbers inside brackets that tell you where a point is.

(x, y)

The first value tells you how far left/right it is from the origin. The second value tells you how far up/down it is from the origin.

What does "y-coordinate" mean?

It's the second value in a coordinate (x,**y**).

What does "x-coordinate" mean?

It's the first value in a coordinate (**x**,y).

How can we use the gradient to see that two lines are perpendicular?

The gradients of perpendicular lines are the negative reciprocal. For example,

What does a table of values tell you?

It tells you a bunch of example coordinates that are on the line you want to draw.

What is a quadrant?

A quarter of the graph.

What does "x-intercept" mean?

Where the line crosses the x-axis.

What does y-intercept mean?

Where the line crosses the y-axis.

What is an independent variable?

It's the variable that **influences** another.

For example, the grade you get on a test *depends on how much you study*. Therefore, the amount you study is an independent variable.

What is a dependent variable?

It's the variable that **depends** on the other.

For example, the grade you get on a test *depends on* how much you study. Therefore, your grade is a dependent variable.

On which axis do we put the independent variable?

The horizontal axis. (The x-axis.)

What does "linear" mean when graphing?

It makes a straight line.

What does an equation of a line do? For example, y=x+3?

It tells you about the relationship of x and y. There are infinite x and y points that make a line. This means that for any x you choose, you can use the equation to find what the y must be in order for the point to be on the line.

What is "gradient-intercept" or "slope-intercept" form?

y=mx+c

In the equation y=mx+c, which letter represents the y-intercept?

(Be careful to notice the sign in front of c. This is also part of the y-intercept.)

In the equation y=mx+c, which letter represents the gradient?

(Be very careful not to include "x". This is only the number BEFORE the x. There is no x in the gradient; it's just a number.)

What are the two methods to graph the equation Ax+By=C?

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- Use algebra to rearrange the formula into gradient-intercept form (y=mx+c).
- Find the intercepts and connect the dots.

What is the gradient of a vertical line?

The gradient of a vertical line is **undefined**.

What is the gradient of a flat horizontal line?

0

(Because we go zero steps up, and 0 ÷ anything=0.)

How can we use the gradient to see that two lines are parallel?

Parallel lines have the same gradient.

How do you know if a given point lies on a given line?

Plug in the x and y values from the point into the equation and see if it works.

How do you calculate the gradient?

How do you graph a line of the form y=mx+c?

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- Mark the y-intercept (which is
*c *from the equation) on the y-axis.
- Use the gradient (which is
*m* from the equation) to count over to the next point.
- Count up/down
- Count over to the right

**from the equation) on the y-axis.***c***from the equation) to count over to the next point.***m*- Count up/down
- Count over to the right

How do you find the equation of a line by looking at the graph?