Question

write an equation of the line that passes through the given point and is parallel to the given line.

1. $(-1, 3); y = -3x + 2$
2. $(1, 2); y = -5x + 4$

Explanation:

Step1: Identify parallel slope

Parallel lines have equal slopes. For problem 3, given line $y=-3x+2$, slope $m=-3$.

Step2: Use point-slope form

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

Step3: Simplify to slope-intercept form

$y-3=-3(x+1)$
$y-3=-3x-3$
$y=-3x-3+3$
$y=-3x$

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Step1: Identify parallel slope

For problem 4, given line $y=-5x+4$, slope $m=-5$.

Step2: Use point-slope form

Substitute $(1,2)$ and $m=-5$ into $y-y_1=m(x-x_1)$:
$y-2=-5(x-1)$

Step3: Simplify to slope-intercept form

$y-2=-5x+5$
$y=-5x+5+2$
$y=-5x+7$

Answer:

1. $y=-3x$
2. $y=-5x+7$