Question

Which line represents the line that passes through (3/2-1/2) and has a slope of 1

Answer 1

Step-by-step explanation:

The point-slope of an equation of a line:

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

m - slope

We have

$m=1\\\\\left(\dfrac{3}{2},\ -\dfrac{1}{2}\right)\to x_1=\dfrac{3}{2},\ y_1=-\dfrac{1}{2}$

Substitute:

$y-\left(-\dfrac{1}{2}\right)=1\left(x-\dfrac{3}{2}\right)$

$y+\dfrac{1}{2}=1\left(x-\dfrac{3}{2}\right)$ → the point-slope form

Convert to the slope-intercept form:

$y+\dfrac{1}{2}=x-\dfrac{3}{2}$         subtract 1/2 from both sides

$y=x-\dfrac{4}{2}$

$y=x-2$ → the slope-intercept form