Answer:
The equation of the line is:
[tex]y = -3x+10[/tex]
The graph is attached below.
Step-by-step explanation:
Given that the line has a slope of -3, so
m = -3
As the point contains the point (4, -2), so we can use the point-slope form of the line equation to determine the line.
Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
so substituting the values m = -3 and the point (4, -2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-2) = -3(x-4)[/tex]
[tex]y+2 = -3x+12[/tex]
[tex]y = -3x+12-2[/tex]
[tex]y = -3x+10[/tex]
Therefore, the equation of the line is:
[tex]y = -3x+10[/tex]
The graph is attached below.
