Answer:
The value of a is "3", to complete the coordinate point (3,7) on the line.
Step-by-step explanation:
We are given the slope of the line, and also one point through which the line passes. Therefore, we can find the actual equation of the line by using the slope-point form of the line:
[tex]y-y_0=m(x-x_0)\\y-(-2)=(-3)(x-6)\\y+2=-3x+18\\y=-3x+18-2\\y=-3x+16[/tex]
Now, we need to find which value of "x" renders a y-value of "7", to complete the coordinate pair (a, 7) as requested. Therefore, we ask for the y-value in the previous equation to be "7", and solve for its associated x-value:
[tex]y=-3x+16\\7=-3x+16\\7-16=-3x\\-9=-3x\\x=\frac{-9}{-3} \\x=3[/tex]
Therefore, x = 3
