Question

QM Q6.) Write the​ slope-intercept equation of the function f whose graph satisifies the given conditions.

Answer 1

Greetings!

The equation of a line in slope-intercept form is:

y = mx + b

m is the slope
b is the y- intercept

What we need to do is to re-arrange 2x - 9y - 18 = 0. We wanna make it looks like y = mx + b

So, the equation is:

2x - 9y - 18 = 0

Subtract 2x - 18 from both sides

→ -9y = -2x + 18

Since we want y, we need to divide both sides by -9

$\frac{-9y}{-9} = \frac{-2x + 18}{-9}$

Thus,

y = 2/9 x - 2 which is in the slope intercept form

Slope m = 2/9 and the y-intercept is = - 2

Given a line with slope m then the slope of a line perpendicular is:

$m_{perpendicular} = - \frac{1}{m}$

$m_{perpendicular} = - \frac{1}{2/9 }$  = - 9/2

Thus,

The equation of the function is:

$y = - \frac{9}{2} x - 2$

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!