Question

How do you write an equation of a line given (-4,2), m=3/2?

Answer 1

Use the equation `y=mx+b`

the slope or `m` is already given therfore the equation now looks like,

`y=3/2x+b`

Solve for `b` by subbing point `P(-4,2)`

`2=3/2*(-4)+b`

`2=-6+b`

`b=8`

Therefore the equation of the line is,

`y=3/2x+8`

graph{3/2x+8 [-10, 10, -5, 5]}

Answer 2

See the entire solution process below:

Explanation:

We can use the point-slope formula to write an equation for this line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substitute the slope and point from the problem gives:

`(y - color(red)(2)) = color(blue)(3/2)(x - color(red)(-4))`

`(y - color(red)(2)) = color(blue)(3/2)(x + color(red)(4))`

We can also transform this equation to the slope-intercept form by solving for `y`. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y - color(red)(2) = (color(blue)(3/2) xx x) + (color(blue)(3/2) xx color(red)(4))`

`y - color(red)(2) = 3/2x + 12/2`

`y - color(red)(2) = 3/2x + 6`

`y - color(red)(2) + 2 = 3/2x + 6 + 2`

`y - 0 = 3/2x + 8`

`y = color(red)(3/2)x + color(blue)(8)`