Question

What is the equation of the line ?

Answer 1

Look at the picture.

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-3, -3) and (2, 0). Substitute:

$m=\dfrac{0-(-3)}{2-(-3)}=\dfrac{3}{5}\\\\y-0=\dfrac{3}{5}(x-2)\qquad|\text{use distributive property}\\\\y=\dfrac{3}{5}x-\dfrac{6}{5}\qquad|\cdot5\\\\5y=3x-6\qquad|-5y\\\\0=3x-5y-6\qquad|+6\\\\3x-5y=6$

Answer:

point-slope form: $y=\dfrac{3}{5}(x-2)$

slope-intercept form: $y=\dfrac{3}{5}x-\dfrac{6}{5}$

standard form: $3x-5y=6$