Question

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

Explanation:

Step1: Identify parallel slope

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

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $(x_1,y_1)=(3,1)$ and $m=\frac{2}{3}$:
$y - 1 = \frac{2}{3}(x - 3)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 1 = \frac{2}{3}x - 2$
$y = \frac{2}{3}x - 2 + 1$
$y = \frac{2}{3}x - 1$

Answer:

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