I'm don't understanding how to solve this question:

The graph of a line passes through the x-intercept of y-20=2/11(x-31) and is perpendicular to the line y=1/7x+7 . The equation of the line, written in Slope-Point form, is y-p = m(x-q). what is the value of m*q ?

just take it step by step. The x-intercept is where y=0, so x = -79

Now, your line must have a slope of -7, so its equation is

y-0 = -7(x+79)
mq = -7(79) = -553

How to get -79 ?

To solve this question, let's break it down into steps:

Step 1: Find the x-intercept of the equation y - 20 = (2/11)(x - 31).
To find the x-intercept, we need to set y = 0 and solve for x.
Let's substitute y = 0 into the equation:
0 - 20 = (2/11)(x - 31)
-20 = (2/11)(x - 31)
Next, multiply both sides of the equation by 11 to eliminate the fraction:
-20 * 11 = 2(x - 31)
-220 = 2x - 62
Then, add 62 to both sides of the equation:
-220 + 62 = 2x
-158 = 2x
Finally, divide both sides by 2 to solve for x:
-158/2 = x
-79 = x
So, the x-intercept of the equation y - 20 = (2/11)(x - 31) is x = -79.

Step 2: Determine the slope of the line y = (1/7)x + 7.
The slope-intercept form of a line is y = mx + b, where m represents the slope.
Comparing y = (1/7)x + 7 to the slope-intercept form, we can see that the slope is m = 1/7.

Step 3: Find the negative reciprocal of the slope.
Since the given line is perpendicular to the line y = (1/7)x + 7, the slopes of the two lines are negative reciprocals of each other.
The negative reciprocal of 1/7 is -7/1, which simplifies to -7.

Step 4: Use the x-intercept and slope to write the equation in the slope-point form y - p = m(x - q).
We have the x-intercept (-79, 0) and the slope -7.
Plugging in these values into the slope-point form, we get:
y - 0 = -7(x - (-79))
Simplifying:
y = -7(x + 79)

Step 5: Observe that in the equation y = -7(x + 79), the value of m * q is -7 * (-79).
-7 * (-79) = 553

Therefore, the value of m * q is 553.