Straight Lines

Question 1

What is a “coordinate”?

Answer 1

It’s two (sometimes 3) numbers inside brackets that tell you where a point is.

(x, y) or (x, y, z)

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.

Question 2

What does “y-coordinate” mean?

Answer 2

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

Question 3

What does “x-coordinate” mean?

Answer 3

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

Question 4

What does “linear” mean when graphing?

Answer 4

It makes a straight line.

Question 5

What does “x-intercept” mean?

Answer 5

Where the line crosses the x-axis.

We know the coordinate is (x, 0).

Question 6

What does y-intercept mean?

Answer 6

Where the line crosses the y-axis.

We know the coordinate is (0, y).

Question 7

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

Answer 7

It describes how steep or slanty a line is.

Question 8

How do you calculate the gradient if you are given two points?

Answer 8

Question 9

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

Answer 9

Parallel lines have the same gradient.

Question 10

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

Answer 10

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

Question 11

What is the equation of a flat horizontal line?

Answer 11

f(x) = ___________

y = __________

Question 12

What is “gradient-intercept” form and why is it the most useful?

Answer 12

y=mx+c

This is the only format the calculator accepts in test mode.

Question 13

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

Answer 13

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

Question 14

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

Answer 14

(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 15

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

Answer 15

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

Question 16

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

Answer 16

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 to the next point.
   
   • Count up/down
   • Count over to the right

Question 17

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

Answer 17

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.

Question 18

How do you calculate the gradient if given a line in standard form?

Answer 18

Rearrange the equation into gradient-intercept form.

Question 19

How do you find the equation of a line, given in the form

Answer 19

Find it in gradient intercept form and rearrnage.

Question 20

What are the steps to find the equation of any line?

Answer 20

1. Write down y = mx + c
2. Figure out the gradient and write it into that equation
   y = 3x + c
3. Plug in any point (1, 2) they gave you and solve for c.
   2 = 3(1)+c
   -1 = c
4. Write down your equation with the m and c that you found.
   y = 3x - 1

Question 21

How do you find the midpoint between two points A and B?

Answer 21

Using the midpoint formula in the formula booklet, separately calculate the x- coordinate and y- coordinate of the midpoint.

Question 22

How do you find some letter coordinate from a point if you already know the line?

Answer 22

Plug the point into the line and solve.

Question 23

How do you find the y-intercept of an equation in standard form?

Answer 23

Plug in 0 for x.

Question 24

How do you find the x-intercept of an equation in standard form?

Answer 24

Plug in 0 for y.

Question 25

How are straight lines related to right anges? For example, "Determine, giving a reason, whether angle ACB is a right angle."

Answer 25

Perpendicular lines make right angles. You should show that the gradients of AC and CB are perpendicular (or not).

Question 26

How do you find the equation of a line parallel to another line? For example, y = 2x + 8?

Answer 26

1. Find the gradient of the original line. This is also the gradient of the new line. 2. Find a point that goes on the line (this is usually given). 3. Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c. 4. Write y=mx+c, where m is the slope and c is the y-intercept.

Question 27

How do you find the equation of a line perpendicular to another line? For example,

Answer 27

1. Identify the gradient of the original line. The gradient of the new line is the negative reciprocal of this. 2. Find a point that goes on the line (this is usually given). 3. Plug the point (x,y) and gradient, m, into the equation y=mx+c and solve for c. 4. Write y=mx+c, where m is the slope and c is the y-intercept.

Question 28

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

Answer 28

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.

Question 29

Answer 29

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

Question 30

How do you rearrange a line equation into the form

Answer 30

1. Multiply EVERYTHING by the biggest denominator. 2. Move all terms to one side.

Question 31

How do you find the distance bewteen 2 points? For example, (0,4) and (8,0)

Answer 31

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

Question 32

How do you find the midpoint of two coordinates?

Answer 32

You plug the points into the midpoint formula from the formula booklet. (Calculate each coordinate one at a time.)

Question 33

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

Answer 33

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

Question 34

What part of a straight line are we talking about when we say "rate of change"?

Answer 34

gradient The gradient represents rate of change. If you're asked to "interpret" the gradient in a real-life situation, say that it represents the rate of change.