Question

A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. y – 5 = 3(x + 1); y = 3x + 8 y + 5 = –3(x – 1); y = –3x – 2

Answer 1

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Answer 2

ANSWER

Point-slope form:

$y + 5 = -3(x - 1)$

Slope-intercept form;

$y = - 3x - 2$

EXPLANATION

The point-slope form of a line is given by:

$y-y_1=m(x-x_1)$

We need to find the slope using the formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Let us substitute the point (1, –5) and (–3, 7).

This implies that,

$m = \frac{7 - - 5}{ - 3 - 1}$

$m = \frac{12}{ - 4} = - 3$

The point slope form now becomes,

$y - - 5 = - 3(x - 1)$

$y + 5 = -3(x - 1)$

To find the slope intercept form, we expand to obtain;

$y = - 3x + 3 - 5$

$y = - 3x - 2$