Answer:
[tex]y = \frac{1}{2} x+5[/tex]
Step-by-step explanation:
1) First, find the slope of the line that passes between the two points. Substitute the x and y values of (2,6) and (-8,1) into slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Then, solve:
[tex]m = \frac{(1)-(6)}{(-8)-(2)} \\m = \frac{1-6}{-8-2} \\m = \frac{-5}{-10} \\m = \frac{1}{2}[/tex]
So, the slope is [tex]\frac{1}{2}[/tex].
2) Now, write the equation of the line using the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex]. Substitute real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{1}{2}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of one of the given points into the formula as well. (Any of the two will do. Either choice will represent the same line. I chose (2,6).) Then, isolate y to put the equation in slope-intercept form and find an answer:
[tex]y-6 = \frac{1}{2} (x-2)\\y-6 = \frac{1}{2} x-1\\y = \frac{1}{2} x+5[/tex]
