Question

instruction: write an equation in slope - intercept form for the line that passes through (-4, 2) and is parallel to a line that passes through (-5, 4) and (-1, 3). step 1: identify the slope of the given line and its parallel slope. step 2: use point - slope form. y - y₁ = m(x - x₁) step 3: convert to slope - intercept form (optional)

Explanation:

Step1: Calculate the slope of the given line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-5,4)$ and $(-1,3)$, we have $x_1=-5,y_1 = 4,x_2=-1,y_2 = 3$. Then $m=\frac{3 - 4}{-1-(-5)}=\frac{-1}{4}=-\frac{1}{4}$. Parallel lines have the same slope, so the slope of the required line is also $m = -\frac{1}{4}$.

Step2: Use the point - slope form

We have the point $(-4,2)$ and $m=-\frac{1}{4}$. Substitute $x_1=-4,y_1 = 2$ into the point - slope form $y - y_1=m(x - x_1)$. We get $y - 2=-\frac{1}{4}(x+4)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=-\frac{1}{4}x - 1$. Add 2 to both sides of the equation: $y=-\frac{1}{4}x+1$.

Answer:

$y = -\frac{1}{4}x + 1$