Question

Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?

Answer 1

The linear equation that respects the given conditions is:

$y = \frac{3}{2}x +$

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.

$2x + 3y = 4$

$3y = -2x + 4$

$y = -\frac{2x}{3} + \frac{4}{3}$

Then:

$-\frac{2}{3}m = -1$

$m = \frac{3}{2}$

Hence:

$y = \frac{3}{2}x + b$

It passes through (−2, 15), that is, when x = -2, y = 15, hence:

$y = \frac{3}{2}x + b$

$15 = \frac{3}{2}(-2) + b$

15 = -3 + b

b = 18.

So the equation is:

$y = \frac{3}{2}x +$

More can be learned about linear functions at brainly.com/question/24808124

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