Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)
To find the slope, you can use the slope formula and plug in the two points:
(-1,5) = (x₁ , y₁)
(5,8) = (x₂ , y₂)
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{8-5}{5-(-1)}[/tex]
[tex]m=\frac{8-5}{5+1} =\frac{3}{6} =\frac{1}{2}[/tex]
y = 1/2x + b
To find "b", plug in either of the points into the equation:
(5,8)
y = 1/2x + b
8 = 1/2(5) + b
8 = 5/2 + b Subtract 5/2 on both sides
8 - 5/2 = b Make the denominators the same in order to subtract them
16/2 - 5/2 = b
11/2 = b
[tex]y = \frac{1}{2}x+\frac{11}{2}[/tex]
The 3rd option is your answer
