Question

Write an equation of the line that passes through the points ( 2,6) and (- 8, 1)

Answer 1

`y = (1)/(2) x+5`

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,
`m = (y_2-y_1)/(x_2-x_1)`. Then, solve:

`m = ((1)-(6))/((-8)-(2)) \\m = (1-6)/(-8-2) \\m = (-5)/(-10) \\m = (1)/(2)`

So, the slope is
`(1)/(2)`.

2) Now, write the equation of the line using the point-slope formula,
`y-y_1 = m (x-x_1)`. Substitute real values for
`m`,
`x_1`, and
`y_1`.

Since
`m` represents the slope, substitute
`(1)/(2)` in its place. Since
`x_1` and
`y_1` 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:

`y-6 = (1)/(2) (x-2)\\y-6 = (1)/(2) x-1\\y = (1)/(2) x+5`