Question

what is the equation of a line parallel to 5x + y = 3 and passing through (3,1)?

Explanation:

Step1: Find the slope of the given line

Rewrite $5x + y=3$ in slope - intercept form $y=-5x + 3$. The slope $m=-5$. Parallel lines have equal slopes, so the slope of the new line is also $m=-5$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(3,1)$ and $m=-5$. Substitute these values: $y - 1=-5(x - 3)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 1=-5x+15$. Then, add 1 to both sides to get the equation in slope - intercept form: $y=-5x + 16$.

Answer:

$y=-5x + 16$