Answer:
-The equation for the problem:
[tex]y = \frac{1}{2}x + \frac{5}{2}[/tex]
Step-by-step explanation:
-First, you need determine the slope of a line:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (where [tex](x_{1},y_{1})[/tex] is the first coordinate and [tex](x_{2},y_{2})[/tex] is the second coordinate).
-Use both points [tex](-1,2)[/tex] and [tex](5,5)[/tex] for the formula:
[tex]m = \frac{5-2}{5+1}[/tex]
[tex]m = \frac{3}{6}[/tex]
[tex]m = \frac{1}{2}[/tex]
-After you have found the slope, use the point-slope formula and use the slope [tex]\frac{1}{2}[/tex] and the first coordinate, which is [tex](-1,2)[/tex], to solve the equation and put it in slope-intercept form:
[tex]y-y_{1} = m (x-x_{1})[/tex]
[tex]y-2 = \frac{1}{2} (x+1)[/tex]
-Solve:
[tex]y-2 = \frac{1}{2} (x+1)[/tex]
[tex]y-2 = \frac{1}{2}x + \frac{1}{2}[/tex]
[tex]y = \frac{1}{2}x + \frac{5}{2}[/tex]
So, therefore the equation is [tex]y = \frac{1}{2}x + \frac{5}{2}[/tex] .
