Question

1. write an equation in slope-intercept form for a line parallel to the equation y = 5x + 4 and contains the point (2, 3)

Explanation:

Step1: Identify parallel line slope

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

Step2: Substitute point into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=5$, $x=2$, $y=3$:
$3 = 5(2) + b$

Step3: Solve for y-intercept $b$

Calculate and isolate $b$:
$3 = 10 + b$
$b = 3 - 10 = -7$

Step4: Write final equation

Substitute $m=5$ and $b=-7$ into $y=mx+b$.

Answer:

$y=5x-7$