Question

Given that the points (-32, - 10) and (-74, 11) lie on a line, what is the equation of the line?

Answer 1

The equation of the line is:

$y=\frac{-1}{2}x-26$

The point-slope equation of a line is given as:

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

where m represents the slope, and is calculated as:

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

For the line passing through the points (-32, - 10) and (-74, 11)

$x_1=-32, y_1=-10, x_2=-74, y_2=11$

Substitute these points into the slope formula to get the slope of the line

$m=\frac{11-(-10)}{-74-(-32)} \\\\m=\frac{11+10}{-74+32} \\\\m=\frac{21}{-42} \\\\m=\frac{-1}{2}$

Substitute $m=\frac{-1}{2}, x_1=-32, y_1=-10$ into the line equation

$y-(-10)=\frac{-1}{2}(x-(-32))\\\\y+10=\frac{-1}{2}x-16\\\\y= \frac{-1}{2}x-16-10\\\\y=\frac{-1}{2}x-26$

The equation of the line is:

$y=\frac{-1}{2}x-26$

Learn more on equation of a line here: brainly.com/question/13763238