Question

What is an equation of the line that passes through the points (0,0) and (5,2)

Answer 1

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

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

Explanation:

1) First, find the slope of the line using the slope formula,
`m = (y_2-y_1)/(x_2-x_1)`. Substitute the x and y values of (0,0) and (5,2) into the formula and simplify like so:

`m = (2-0)/(5-0) \\m = (2)/(5)`

So, the slope is
`(2)/(5)`.

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

Since
`m` represents the slope, substitute
`(2)/(5)` in its place. Since
`x_1` and
`y_1` represent the x and y values of a point the line intersects, we can substitute the x and y values of one of the given points (I chose (0,0)) into the formula as well. Then, isolate y to put in slope-intercept form:

`y-0=(2)/(5) (x-0)\\y = (2)/(5) x`