Question

find in the form y-mx +c, the equation of a line:
perpendicular to y =6-x passing through (-4,3) ?

Answer 1

For a line in the form y = mx + b, m = slope.

Follow these steps:
1. Find the slope of the given line.
2. Find the slope of the perpendicular line.
3. Find the equation of the perpendicular line.

For step 1, write the given equation in y = mx + b form. That will give you the slope of the given line.

For step 2, the slopes of perpendicular lines are negative reciprocals. That means their product is -1. That also means that if you have the slope of a line, and you want the slope of a perpendicular, write the given slope as a fraction, then flip it, then change the sign.

For step 3, use the slope of the perpendicular and the given point in y = mx + b, and solve for b.

Answer 2

isn't the gradient x? its so confusing..i don't know what the slope of the given line is

Answer 3

The slope of a line is a measure of the inclination of a line.
A line with slope = zero is horizontal.
A line with a positive slope goes up to the right.
A line with negative slope goes down to the right.
A vertical line has undefined slope.

Answer 4

Start with your given line, y = 6 - x.
Can you write the equation in y = mx + b form?

Answer 5

y=x -6?

Answer 6

You're on the right track, but you need to be careful.
You can't just change the right side from 6 - x to x - 6. They are not the same thing.
For example, 9 - 6 is not the same as 6 - 9.
9 - 6 = 3
6 - 9 = -3
3 and -3 are different, so 9 - 6 is not the same as 6 - 9.

Answer 7

Think of the right side like this:
y = 6 - x
is the same as
y = 6 + (-x)

Now use the commuttative property of addition on the right side to change the order of 6 and -x.

Answer 8

y= -x+6

Answer 9

Great.
Now compare that with y = mx + b

Answer 10

What is m, the slope of the given equation.

Answer 11

Remember that x is the same as 1x, and -x is the same as -1x.
You can think of the given equation as
y = -1x + 6
Now compare that with
y = mx + b
Now can you tell what m is?

Answer 12

-1?

Answer 13

Correct.
You know the slope of the given line is -1.
Now we can go to step 2.

Answer 14

Write the slope of the given line as a fraction. What is -1 written as a fraction?

Answer 15

-1/1

Answer 16

Great. Now flip it and change the sign. What do you get?

Answer 17

1/-1

Answer 18

isn't it 1? the negative reciprocal

Answer 19

Correct. The slope of the perpendicular line is simply 1.

Answer 20

yes!

Answer 21

Now we can go on to step 3.

Answer 22

so its y= x + ?

Answer 23

Correct. Now we use the slope and the point to do step 3.

You need to find the equation of the line that has slope 1
and passes through point (-4, 3)

Answer 24

We use the slope-intercept form, y = mx+ b, and we plug in everything we know.
(x, y) = (-4, 3); m = 1

y = mx + b
3 = 1(-4) + b

Now solve for b.

Answer 25

is it 7?

Answer 26

so y= x +7?

Answer 27

Correct.
3 = 1(-4) + b
3 = -4 + b
7 = b
b = 7

Now that we know b = 7, we rewrite the equation with our known slope and b:
y = x + 7

Answer 28

thanks!

Answer 29

wlcm