Question

2.5 parallel and perpendicular lines: problem 6
(1 point)
the equation of the line that goes through the point (3,2) and is parallel to the line 3x + 2y = 4 can be written in the form y = mx + b where m is
and where b is
note: you can earn partial credit on this problem.
preview my answers submit answers
you have attempted this problem 0 times.
you have unlimited attempts remaining.
email instructor

Explanation:

Step1: Find the slope of the given line

Rewrite $3x + 2y=4$ in slope - intercept form $y=mx + b$.
$2y=-3x + 4$, so $y=-\frac{3}{2}x+2$. The slope of the given line is $m_1 =-\frac{3}{2}$. Since parallel lines have the same slope, the slope $m$ of the required line is $m =-\frac{3}{2}$.

Step2: Find the y - intercept of the required line

We know the line passes through the point $(3,2)$ and has slope $m =-\frac{3}{2}$. Substitute $x = 3$, $y = 2$ and $m=-\frac{3}{2}$ into $y=mx + b$.
$2=-\frac{3}{2}\times3 + b$.
$2=-\frac{9}{2}+b$.
$b=2+\frac{9}{2}=\frac{4 + 9}{2}=\frac{13}{2}$.

Answer:

$m =-\frac{3}{2}$, $b=\frac{13}{2}$