Answer:
[tex]\boxed {\boxed {\sf y=-7x-9}}[/tex]
Step-by-step explanation:
Since we are given a point and the slope, we should use the point-slope formula.
[tex]y-y_1=m(x-x_1)[/tex]
where (x₁, y₁) is the point the line passes through and m is the slope.
We know the line passes through the point (-3, 12) and the slope is -7. Therefore,
Substitute the values into the formula.
[tex]y-12=-7(x--3)[/tex]
Remember that 2 back to back negative signs become a positive.
[tex]y-12=-7(x+3)[/tex]
Now we have to put the equation in slope-intercept form, or y=mx+b. Therefore, we need to isolate the variable y on one side of the equation.
First, distribute the -7. Multiply each term inside the parentheses by -7.
[tex]y-12=(-7*x)+ (-7*3) \\y-12= (-7x)+(-21) \\y-12= -7x-21[/tex]
12 is being subtracted from y. The inverse operation of subtraction is addition. Add 12 to both sides of the equation.
[tex]y-12+12=-7x-21+12\\y= -7x-21+12\\y=-7x-9[/tex]
The equation of the line is y=-7x-9
