Question

Pls help! Write an equation of the line that passes through the points (1, 2) and (4, 8)

Answer 1

Answer (assuming it can be in slope-intercept form):

`y =2x`

Explanation:

1) First, find the slope of the line. 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 = ((8)-(2))/((4)-(1)) \\m = (8-2)/(4-1) \\m = (6)/(3) \\m = 2`

So, the slope is 2.

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

Since
`m` represents the slope, substitute 2 in its place. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, choose one of the given points (it doesn't matter which one, the results will equal the same thing) and substitute its x and y values into the formula as well. (I chose (1,2), as seen below.) Then, isolate y to put the equation in slope-intercept form (
`y = mx + b` format) and find the following answer:

`y-(2) = 2 (x-(1))\\y-2 = 2(x-1)\\y -2 = 2x-2\\y = 2x+0\\y = 2x`