Question

If a line has a slope of - 3 and goes through the point (-4,10), then theequation for the line in slope-intercept form is

Answer 1

The slope-intercept form of the line has the following form below:

`y=mx+b`

In the question, the data given are:

slope = -3

point = (-4, 10)

y - coordinate = 10

x - coordinate = -4

To be able to solve the equation of the line given slope and a point, we can use the following formula below:

`y-y_1=m(x-x_1)`

where:

m = slope

y₁ = y - coordinate of the point that goes through the line

x₁ = x - coordinate of the point that goes through the line

Let's substitute the given data with the formula we have.

`\begin{gathered} y-10=-3(x--4) \\ y-10=-3(x+4) \\ \text{Distribute -3 to the values inside the parenthesis.} \\ y-10=-3x-12 \\ \text{Add 10 on both sides of the equation.} \\ y-10+10=-3x-12+10 \\ y=-3x-2 \end{gathered}`

Therefore, the equation of this line in slope-intercept form is:

y = -3x - 2.