Find the equation of a line that is perpendicular to line g that contains (p, q). a) 4x + y = q + 4p b) x − 4y = −4q + p c) −4x + y = q − 4p d) x + 4y = 4q + p

D. x + 4y = 4Q + P

Step-by-step explanation:

In order to find an equation perpendicular to line g, we need to know the equation for line g.  We can use the slope-intercept form of a line and fill it in with the info from the graph.  The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.  From our graph we can see that the y-intercept is at (0, 14), so b = 14.  Looking at the 2 other points on the line (one of them NOT being the y-intercept at (0, 14)), we can determine the slope.  From the point (-3, 2), we go up 4 units and over 1 unit to the right to get to the next point, which is (-2, 6).  That means that the slope of line g is 4/1 which is of course just 4.  Now we have an equation for line g:

y = 4x + 14

The perpendicular slope to this line is the opposite reciprocal so the slope of the perpendicular line is -1/4.  We can now use that perpendicular slope along with (P, Q) in the point-slope form of a line to get our answer.

Simplifying a bit gives us:

.

Multiply everything through by 4 to get rid of the fractions:

4y - 4Q = -x + P

Now get the x and y terms on one side:

x + 4y = 4Q + P

That's choice D

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