Answer :
The slope-intercept form of the line has the following form below:
[tex]y=mx+b[/tex]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:
[tex]y-y_1=m(x-x_1)[/tex]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.
[tex]\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}[/tex]Therefore, the equation of this line in slope-intercept form is:
y = -3x - 2.