Question

Instructions: Find the equation of the line through point (2, -1) and

Answer 1

Answer:

$y = -\frac{2}{5}x -\frac{1}{5}$

Step-by-step explanation:

Given

Passes through: $(2,-1)$

Parallel to: $2x + 5y = 15$

Required

First, calculate the slope of the parallel line

$2x + 5y = 15$

Make y the subject

$5y = 15 - 2x$

Divide through by 5

$y = 3 - \frac{2}{5}x$

$y =- \frac{2}{5}x+3$

An equation in slope intercept has the form:

$y = mx + b$

Where:

m = slope

$y = mx + b$

So:

$m = -\frac{2}{5}$

The required is parallel to $2x + 5y = 15$.

This mean, the same slope

The equation is the calculated using:

$y - y_1 = m(x - x_2)$

This gives:

$y - (-1) = -\frac{2}{5}(x - 2)$

$y +1 = -\frac{2}{5}x +\frac{2}{5}*2$

$y +1 = -\frac{2}{5}x +\frac{4}{5}$

$y = -\frac{2}{5}x +\frac{4}{5}-1$

Take LCM

$y = -\frac{2}{5}x +\frac{4-5}{5}$

$y = -\frac{2}{5}x -\frac{1}{5}$

i.e.

$y = -2/3x -1/5$