Equation Of A Line

Question 1

Draw the line y=2x+1 between -3,3

Answer 1

Draw a table of values to create co-ordinates to plot
X|-3|-2|-1|0|1|2|3 (-3 to 3)
Y|-5|-3|-1|1|3|5|7 (2x3+1)

Number in front of x controls the gradient
The +/- number controls where the line will cross the y axis

Draw the graph (check book for correct answer

Question 2

What is the equation for every straight line?

Answer 2

Y=mx+c

Question 3

In y=mx+c

What does m tell you? What does c tell you?

Answer 3

M is the gradient (steepness) of the line

+c is where it crosses the y axis (y intercept)

Question 4

What is the gradient and why intercept of the following lines?
Y=4x-1
Y=3+2x
Y=5-3x
2y=6x-4
X=4y+12

Answer 4

Gradient,Y intercept
Y=4x-1.    | 4,-1
Y=3+2x.   |2,3
Y=5-3x.    |-3,5
2y=6x-4.  |3,-2
X=4y+12   |1/4,-3
^ goes to x-12=4y goes to 1x/4 -3=y
                                                 ^ this means it will go up 1/4 for every one you go across

Question 5

What is the gradient and y intercept of 8x-4y+10=0

Answer 5

/+4y
8x+10=4y
/divide by 4
2x+2.5=y

Gradient =2 y intercept =2.5

Question 6

How can you tell if lines will be parallel

Answer 6

They will have the same gradient

Question 7

A line is parallel to y=3x+2 and passes through the point (4,11) find the equation of the line

Answer 7

Because it’s parallel the line will be of the format y=3x+c

Substitute in the coordinate (4,11) to find what c needs to be

Y=3x+c
11=3x4+c
11=12+c
/-12
-1=c

Therefore equation of the line is y=3x-1

Question 8

We know the gradient of a line. What will it’s perpendicular gradient be?

Answer 8

The negative reciprocal of it

Question 9

How do perpendicular lines cross each other?

Answer 9

At right angles

Question 10

Gradient is 2/3. What is the perpendicular gradient?

Answer 10

-3/2

Question 11

Gradient is -4/3. What is the perpendicular gradient?

Answer 11

3/4

Question 12

Gradient is 7. What is the perpendicular gradient?

Answer 12

-1/7

Question 13

Gradient is -2. What is the perpendicular gradient?

Answer 13

1/2

Question 14

Find the equation of a line that is perpendicular to y=-1/3x+1 and passes through (6,1)

Answer 14

Y=3x+2
1=3x6+c
1=18+c
-17=c
Y=3x-17

Question 15

Work out the gradient between (-1,12) and (2,6)

Answer 15

ys: 12-6=6
xs: -1-2=-3

6/-3=-2

Question 16

What is the equation for working out gradient of a line between two points (x,y) and (x2,y2)

Answer 16

Gradient = y2-y/x2-x = difference in ys/difference in xs

Question 17

Work out the gradient of the line between the points (3,4) and (5,2)

Answer 17

Gradient = 2-4/5-3=-2/2=-1

Question 18

Work out the equation of the line between (-1,5) and (2,17)

Answer 18

Gradient = 17-5/2--1 = 12/4
Y=mx+c
Y=4x+c
(Sub in 1 of the coordinates
17=4x2+c
17=8+c
9=c

Y=4x+9

Question 19

What’s the equation for midpoint of 2 coordinates, (X1,1) and (x2,y2)?

Answer 19

(X1+x2/2, y1+y2/2)

Question 20

Find the midpoint of the line segment between the points (-3,8)and(4,-5)

Answer 20

Midpoint (-3+4/2, 8+-5/2)

=(1/2,3/2)