Determine the equation of the line that has a slope of -4 and passes through the point (-8, 6)
The equation of a line can be written in slope-intercept form, which is of the form y = mx + b, where m is the slope and b is the y-intercept.
To determine the equation of the line that has a slope of -4, we substitute the value of the slope (-4) into the equation as follows:
y = -4x + b
We know that the line passes through the point (-8, 6), which means that when x = -8 and y = 6, the equation should hold true. Substituting these values into the equation, we get:
6 = -4(-8) + b
Simplifying the right side of the equation:
6 = 32 + b
Subtracting 32 from both sides of the equation:
-26 = b
Finally, substituting the value of b (-26) back into the equation y = -4x + b, we get the equation of the line:
y = -4x - 26