Final answer:
The equation of the line that passes through the point (5, 19) with a slope of -12 is y = -12x + 79. This is found using the slope-intercept form y = mx + b, substituting the slope (m) and solving for the y-intercept (b) using the given point.
Step-by-step explanation:
To find the equation of the line that passes through the point (5, 19) with a slope of -12, we can use the slope-intercept form of a line, which is y = mx + b. In this equation, m is the slope, and b is the y-intercept, the point where the line crosses the y-axis. Given that the slope m is -12, we can substitute the given point into the equation to find b.
Starting with the slope-intercept form:
y = mx + b
Substitute m = -12 and the point (5, 19):
19 = (-12)(5) + b
This gives us:
19 = -60 + b
Adding 60 to both sides to solve for b:
b = 19 + 60
b = 79
Now we have both m and b, so we can write the equation of the line:
y = -12x + 79