Question

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

`y = (1)/(4) x`

Explanation:

1) First, find the slope of the equation. Use the slope formula
`m= (y_2-y_1)/(x_2-x_1)`. Substitute the x and y values of the given points into the formula and solve:

`m = ((2)-(1))/((8)-(4)) \\m = (2-1)/(8-4)\\m = (1)/(4)`

Thus, the slope is
`(1)/(4)`.

2) Now, use the point-slope formula
`y-y_1 = m (x-x_1)` to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for
`m`,
`x_1`, and
`y_1`.

Since
`m` represents the slope, substitute
`(1)/(4)` for it. Since
`x_1` and
`y_1` represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

`y-(1) = (1)/(4) (x-4)\\y-1 = (1)/(4) x-1\\y = (1)/(4) x+0\\y=(1)/(4)x`