Question

Write an equation (in slope-intercept form) of the line that passes through (0, 3) and (−5, 2.5).

Answer 1

The equation of the line passing throught the points $A(x_A,y_A)$ and $B(x_B,y_B)$ has a form

$\dfrac{x-x_A}{x_B-x_A}=\dfrac{y-y_A}{y_B-y_A}.$

Now the equation of the line passing through points (0, 3) and (−5, 2.5) is

$\dfrac{x-0}{-5-0}=\dfrac{y-3}{2.5-3}.$

Simplify it:

$\dfrac{x}{-5}=\dfrac{y-3}{-0.5},\\ \\0.5x=5(y-3),\\ \\5x=50y-150,\\ \\x=10y-30,\\ \\10y=x+30,\\ \\y=0.1x+3.$

This equation is in slope-intercept form.

Answer: y=0.1x+3.