Greetings!
We can use these points to find the slope of a line, using the slope formula: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Input the points:
[tex]m= \frac{(5)-(2)}{(0)-(-2)}[/tex]
Combine like terms:
[tex]m= \frac{3}{2}[/tex]
The Slope is Equal to:
[tex]\boxed{\frac{3}{2}}[/tex]
To find the y-intercept of the line, we use the slope and the points. First, arrange the equation is slope y-intercept form:
[tex]y=mx+b[/tex]
Input the slope and one of the points:
[tex](5)=\frac{3}{2}(0)+b[/tex]
Combine like terms:
[tex](5)=b[/tex]
The y-intercept is Equal to:
[tex]\boxed{5}[/tex]
The Equation of the Line Is:
[tex]\boxed{y=\frac{3}{2}x+5}[/tex]
I hope this helped!
-Benjamin
