Question

Line m passes through point (–2, –1) and is perpendicular to the graph of y = –23x + 6. Line n is parallel to line m and passes through point (4, –3). Which is the equation of line n in slope-intercept form?

Answer 1

$\huge\boxed{y=\frac{1}{23}x-\frac{73}{23}}$

First, find the slope perpendicular to $-23$. We can do this by finding the opposite reciprocal.

Multiply the slope by $-1$ and write the result as a fraction.

$-23*-1=23=\frac{23}{1}$

Flip the numerator and the denominator.

$\frac{23}{1}\longrightarrow\frac{1}{23}$

This is the slope of line $m$. Since lines $m$ and $n$ are perpendicular, this is also the slope of line $n$.

Write the formula for point-slope form.

$y-y_1=m(x-x_1)$

Substitute in the values for line $n$.

$y-(-3)=\frac{1}{23}(x-4)$

Simplify the negative subtraction.

$y+3=\frac{1}{23}(x-4)$

Distribute the $\frac{1}{23}$ to the $(x-4)$.

$y+3=\frac{1}{23}x-\frac{4}{23}$

Subtract $3$ — which is equivalent to $\frac{69}{23}$ — from both sides.

$\boxed{y=\frac{1}{23}x-\frac{73}{23}}$