Question

write an equation of the line that passes through (1,2) and is parallel to the line y = -5x + 4. y = \square

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=-5x+4$, the slope $m=-5$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-5$, $(x_1,y_1)=(1,2)$:
$y - 2 = -5(x - 1)$

Step3: Simplify to slope-intercept form

Expand and rearrange:
$y - 2 = -5x + 5$
$y = -5x + 5 + 2$
$y = -5x + 7$

Answer:

$y = -5x + 7$