What does "gradient" 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 "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" form for a line?

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.
- Find the x-intercept by pluggin in y=0 and solving for x.
- Find the y-intercept by plugging in x=0 and solving for y.

- Find the x-intercept by pluggin in y=0 and solving for x.
- Find the y-intercept by plugging in x=0 and solving for y.

What is the equation of a vertical line?

x = ________.

What is the equation of a flat horizontal line?

f(x) = ___________

y = __________

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 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 perpendicular to another line?

For example,

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- Identify the gradient of the original line. The gradient of the new line is the negative reciprocal of this.
- Find a point that goes on the line (this is usually given).
- Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c.
- Write y=mx+c, where m is the slope and c is the y-intercept.

How do you find the equation of a line parallel to another line?

For example, y = 2x + 8?

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- Find the gradient of the original line. This is also the gradient of the new line.
- Find a point that goes on the line (this is usually given).
- Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c.
- Write y=mx+c, where m is the slope and c is the y-intercept.

How do you find the equation of a line?

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- Find the gradient.
- Find a point that goes on the line (this is usually given).
- Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c.
- Write y=mx+c, where m is the slope and c is the y-intercept.

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

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- Look at the graph to find the y-intercept.
- Find a second point that goes through a perfect coordinate.
- Find the slope by count how far up/down and how far right you go from the left point to the right point.
- Write y=mx+c, where m is the slope and c is the y-intercept.

Plug the point (8,y) into your line equation and solve for y.

How do you rearrange a line equation into the form

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- Multiply EVERYTHING by the biggest denominator.
- Move all terms to one side.

How do you find the distance bewteen 2 points?

For example, (0,4) and (8,0)

Either create a right-angled triangle on the graph and use the pythagorean theorem or use the distance formula in the booklet.

How do you find a variable, given the midpoint of two coordinates?

For each coordinate separately, you plug the points into the midpoint formula and solve.