Remember that in the equation y = mx + b, m represents the slope of the line and b represents the y-intercept of the line.
To find the equations of lines that are parallel and perpendicular to a given line, the first step is to identify the slope of your given line. The given line is y = 9x - 7. The slope of the line is the coefficient of x (the number in front of x), so the slope of the given line is 9.
(The y-intercept of the given line won't matter when figuring out the rest of the question.)
QUESTION 1: PERPENDICULAR LINE
Remember that the slope of perpendicular lines are NEGATIVE RECIPROCALS of each other.
That means that since the slope of our given line is 9, the slope of the line that is perpendicular to our given line is -1/9.
If we substitute that into the equation directly, now we have y = (-1/9) x + b.
The line is supposed to pass through (5, 2), so we will substitute this coordinate in the (x, y) of the equation:
2 = (-1/9) (5) + b
2 = -5/9 + b
23/9 = b
So the equation of the PERPENDICULAR line is y = -1/9 x + 23/9
QUESTION 2: PARALLEL LINE
Remember that the parallel lines have the SAME SLOPE.
That means that since the slope of our given line is 9, the slope of the line that is parallel to our given line is also 9.
If we substitute that into the equation directly, we have y = 9x + b.
The line is supposed to pass through (5, 2), so we will substitute this coordinate in the (x, y) of the equation:
2 = (9) (5) + b
2 = 45 + b
-43 = b
So the equation of the PARALLEL line is y = 9x - 43
