Coordinate Geometry (HL App)

Question 1

What does “gradient” or “slope” describe in normal English words?

Answer 1

It describes how steep or slanty a line is.

Question 2

What is a “coordinate”?

Answer 2

2D

It’s two or three 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.

3D

(x,y,z)

• The first value tells about the across direction.
• The second value tells about the depth direction.
• The third value tells you about the height direction.

Question 3

What does “y-coordinate” mean?

Answer 3

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

Question 4

What does “x-coordinate” mean?

Answer 4

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

Question 5

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

Answer 5

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

Question 6

What does a table of values tell you?

Answer 6

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

Question 7

What is a quadrant?

Answer 7

A quarter of the graph.

Question 8

What does “x-intercept” mean?

Answer 8

Where the line crosses the x-axis.

Question 9

What does y-intercept mean?

Answer 9

Where the line crosses the y-axis.

Question 10

What is an independent variable?

Answer 10

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.

Question 11

What is a dependent variable?

Answer 11

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.

Question 12

On which axis do we put the independent variable?

Answer 12

The horizontal axis. (The x-axis.)

Question 13

What does “linear” mean when graphing?

Answer 13

It makes a straight line.

Question 14

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

Answer 14

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.

Question 15

What is “gradient-intercept” or “slope-intercept” form?

Answer 15

y=mx+c

Question 16

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

Answer 16

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

Question 17

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

Answer 17

(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.)

Question 18

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

Answer 18

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

Question 19

What is the gradient of a vertical line?

Answer 19

The gradient of a vertical line is undefined.

Question 20

What is the gradient of a flat horizontal line?

Answer 20

0

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

Question 21

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

Answer 21

Parallel lines have the same gradient.

Question 22

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

Answer 22

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

Question 23

How do you calculate the gradient?

Answer 23

Question 24

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

Answer 24

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

Question 25

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

Answer 25

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