Question

How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

Answer 1

`y = 5/2x + 41/2`

Explanation:

First, build the equation using the information given, the slope and a point, using the point-slope formula.

The point-slope formula states: `color(red)((y - y_1) = m(x - x_1))`
Where `color(red)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the information from the problem gives the equation:

`y - 3 = 5/2(x - -7)`

`y - 3 = 5/2(x + 7)`

The slope-intercept for of a linear equation is `color(red)(y = mx + b)` where `color(red)(m)` is the slope and `color(red)(b)` is the y-intercept.

To transform our equation we must solve for `y` while keeping the equation balanced:

`y - 3 = 5/2x + (5/2 xx 7)`

`y - 3 = 5/2x + 35/2`

`y - 3 + color(red)(3) = 5/2x + 35/2 + color(red)(3)`

`y - 0 = 5/2x + 35/2 + (3 xx 2/2)`

`y = 5/2x + 35/2 + 6/2`

`y = 5/2x + (35 + 6)/2`

`y = 5/2x + 41/2`