Question

Write an equation in slope-intercept form for a line perpendicular to the graph of the equation that passes through the x-intercept of that line. y=2/3-6

Answer 1

is the slope 2/3 and the y-intercept-6

Answer 2

-3/2

Answer 3

so would it be y=-3/2+6

Answer 4

If it is not clear we can start from the beginning.

Answer 5

can we im so confused

Answer 6

Sure. No problem

Answer 7

y = 2/3x - 6 is the equation of the line.

The general equation of a line is y = mx + b where m is the slope of the line and b is the Y intercept. y intercept just means that is where the graph will cut the y axis.

But here they are interested in the x intercept. x intercept means where does the line cut the axis? To find that all we have to do is set y = 0. Why y = 0? Because all points on x axis has y = 0.

Answer 8

So let us find the x intercept of y = 2/3x - 6 by setting y = 0 and solving for x.
0 = 2/3x - 6
Add 6 to both sides
6 = 2/3x
multiply both sides by 3
18 = 2x
divide both sides by 2
9 = x.
So the x intercept is 9. That is where the line cuts the x axis. And at that point the y value will be 0. So the point will be (9, 0)

Answer 9

so would it be y=9x+0

Answer 10

No. What we found was the point where the original line cuts the x axis.
I will show it in a drawing:

Answer 11

We did the calculations so far to find the x intercept of the line y = 2/3x - 6
The point where it cuts the x axis is (9,0)

Now we need to find the equation of a line that is perpendicular to the original line and also passes through (9,0)

Answer 12

The slope of the line y = 2/3x - 6 is: 2/3

The slope of the perpendicular line will be the negative reciprocal of the slope of the original line. So it is -3/2

Put it in y = mx + b
y = -3/2x + b

Answer 13

The perpendicular line passes through (9, 0). So put x = 9 and y = 0 in y = -3/2x + b and solve for b.

Answer 14

y = -3/2x + b x = 9, y = 0
0 = (-3/2)(9) + b
0 = -27/2 + b
b = 27/2
Put it in y = -3/2x + b
and you get:

y = -3/2x + 27/2

This is the equation of the line that is perpendicular to the original line and passes through the x intercept of the original line.

Answer 15

This is how the two lines will look when graphed: