Question

Write an equation for the line that is perpendicular to the line x-3y=9 at the x-intercept.

Answer 1

First find the x-intercept.
To do that, set y = 0 and solve for x. That will be the x-intercept.

Answer 2

okay so x=9

Answer 3

Yes, the x-intercept is 9 and the point is (9,0) (because on the x-axis, which is where the x-intercept is, y = 0).

Next, we need to find the slope of the line x-3y=9. Put it in the slope-intercept form y = mx + b so we can find the slope 'm'.

Answer 4

x - 3y = 9
add 3y to both sides:
x = 9 + 3y
add -9 to both sides:
x - 9 = 3y
divide both sides by 3:
1/3 * x - 3 = y or
y = 1/3 * x - 3

What is the slope of the line y = 1/3 * x - 3 ?
Compare it to y = mx + b where 'm' is the slope.

Answer 5

the slope is 1/3. So do i replace the m with the 1/3 and the b with a 0?

Answer 6

The slope of this line is 1/3.

What will be the slope of a line that is perpendicular to the above line?

Answer 7

it would be -3

Answer 8

Correct. So you know now the slope of the line is -3 and that it passes through the point (9,0) found earlier. What is the equation of this line?

Answer 9

it would be y=-3x?

Answer 10

y = mx + b
m = -3
y = -3x + b ---- (1)
It passes through the point (9, 0).
when x = 9, y = 0. Put it in (1).
0 = -3(9) + b
0 = -27 + b
b = 27

y = -3x + 27 is the answer in slope-intercept form.
3x + y = 27 is the answer in standard form.

Answer 11

thank you so so so much!! :)

Answer 12

You are welcome.