Question

what is an equation of the line that passes through the point (3,1) and is parallel to the line 2x + 3y = 24?

Explanation:

Step1: Find the slope of the given line.

Rewrite $2x + 3y=24$ in slope - intercept form $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept).
$3y=-2x + 24$, so $y=-\frac{2}{3}x+8$. The slope of the line $2x + 3y = 24$ is $m=-\frac{2}{3}$. Since parallel lines have the same slope, the slope of the new line is also $m = -\frac{2}{3}$.

Step2: Use the point - slope form to find the equation of the new line.

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(3,1)$ and $m = -\frac{2}{3}$.
Substitute the values: $y - 1=-\frac{2}{3}(x - 3)$.

Step3: Simplify the equation.

Expand the right - hand side: $y - 1=-\frac{2}{3}x+2$.
Add 1 to both sides to get the equation in slope - intercept form: $y=-\frac{2}{3}x + 3$.

Answer:

$y=-\frac{2}{3}x + 3$