Question

What is the equation of the line that passes through the points (-2, 2) and (0, 5)?

Answer 1

Greetings!

We can use these points to find the slope of a line, using the slope formula: $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Input the points: 
$m= \frac{(5)-(2)}{(0)-(-2)}$

Combine like terms:
$m= \frac{3}{2}$

The Slope is Equal to:
$\boxed{\frac{3}{2}}$

To find the y-intercept of the line, we use the slope and the points. First, arrange the equation is slope y-intercept form:
$y=mx+b$

Input the slope and one of the points:
$(5)=\frac{3}{2}(0)+b$

Combine like terms:
$(5)=b$

The y-intercept is Equal to:
$\boxed{5}$

The Equation of the Line Is:
$\boxed{y=\frac{3}{2}x+5}$

I hope this helped!
-Benjamin