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

see picture attached.

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Answer 2

Point-slope form:

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

Slope-intercept form;

`y = - 3x - 2`

Step-by-step 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 = (y_2-y_1)/(x_2-x_1)`

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

This implies that,

`m = (7 - - 5)/( - 3 - 1)`

`m = (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`