ANSWER
Point-slope form:
[tex]y + 5 = -3(x - 1)[/tex]
Slope-intercept form;
[tex]y = - 3x - 2[/tex]
EXPLANATION
The point-slope form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We need to find the slope using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let us substitute the point (1, –5) and (–3, 7).
This implies that,
[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]
[tex]m = \frac{12}{ - 4} = - 3[/tex]
The point slope form now becomes,
[tex]y - - 5 = - 3(x - 1)[/tex]
[tex]y + 5 = -3(x - 1)[/tex]
To find the slope intercept form, we expand to obtain;
[tex]y = - 3x + 3 - 5[/tex]
[tex]y = - 3x - 2[/tex]
