Question

write the equation of a line through (3,1), parallel to $y = \frac{2}{3}x + 1$
$y = \square x + \square$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line is $y=\frac{2}{3}x + 1$, so the slope $m=\frac{2}{3}$.

Step2: Substitute point into slope-intercept form

Use $y=mx+b$, substitute $(x,y)=(3,1)$ and $m=\frac{2}{3}$:
$1=\frac{2}{3}(3)+b$

Step3: Solve for y-intercept b

Calculate $\frac{2}{3}(3)=2$, then $1=2+b$, so $b=1-2=-1$.

Step4: Write final line equation

Substitute $m=\frac{2}{3}$ and $b=-1$ into $y=mx+b$.

Answer:

$y=\frac{2}{3}x + (-1)$ or simplified as $y=\frac{2}{3}x - 1$