Answer:
C. 7x + y = -19
Explanation:
Pre-Solving
We are given that a line has a slope (m) of -7 and passes through (-2, -5).
We want to write the equation of this line in the form ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0.
Solving
To start, we can write the equation of the line in slope-intercept form, which is y=mx+b where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope, we can plug that into the equation.
Substitute -7 as m in the equation.
y = -7x + b
Now, we need to find b.
As the line passes through (-2, -5), we can use the values of the point to help solve for b.
Substitute -2 as x and -5 as y.
-5 = -7(-2) + b
Multiply.
-5 = 14 + b
Subtract 14 from both sides.
-19 = b
Substitute 9 as b.
y = -7x - 19
Now, add 7x to both sides.
7x + y = -19
The answer is C.