Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as fractions, if necessary. passes through (−7,−4), perpendicular to y=12x+9

Answer 1

Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as fractions, if necessary. passes through (−7,−4), perpendicular to y=12x+9

One thing to always remember is that lines that are PARALLEL have the SAME SLOPE. Lines that are PERPENDICULAR have SLOPES that are NEGATIVE INVERSES of each other. This information will serve you well in your math classes.

The slope of the line defined by y = 12x + 9, which is written in slope-intercept form, is the coefficient of the x-term, so it is 12.

So, the line that you are asked to describe has a slope that is the negative reciprocal of 12, which is –1/12. Thus, the beginning of your perpendicular line is y = (–1/12)x + b.

All, we need to figure out now is the value of b. We do this by substituting for x and y the values identified by the point specified, (–7, –4), and solving for b.

–4 = (–1/12)(–7) + b

–4 = (7/12) + b

–4 – (7/12) = (7/12) – (7/12) + b

(–48/12) – (7/12) = b

–55/12 = b

We now substitute b into the above equation for the perpendicular line y = (–1/12)x + b to get the equation for the perpendicular line that passes through (–7, –4).

y = (–1/12)x – (55/12)

Answer 2

perpendicular line has negative inverse slope = -1/12

y=(-1/12)x + b, plug in the point to solve for b

-4 = (-1/12)(-7) + b

b =-4 - 7/12 = -48/12 -7/12 = -55/12

y = (-1/12)x - 55/12 is the perpendicular line through the given point