Question

card 4
the graph of a line goes through the points
(-4, 10) and (-2, -6).
a what is the slope of the line?
b what is the y-intercept of the line?
c write an equation for this line.

Explanation:

Step1: Find the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-4, 10)$ and $(x_2, y_2) = (-2, -6)$. Then $m = \frac{-6 - 10}{-2 - (-4)} = \frac{-16}{2} = -8$.

Step2: Find the y-intercept

Use the point-slope form $y - y_1 = m(x - x_1)$. Substitute $m = -8$, $x_1 = -4$, $y_1 = 10$: $y - 10 = -8(x + 4)$. Simplify: $y - 10 = -8x - 32$, so $y = -8x - 22$. The y-intercept is $-22$.

Step3: Write the equation

From Step2, the equation is $y = -8x - 22$.

Answer:

a. The slope is $-8$.
b. The y - intercept is $-22$.
c. The equation is $y = -8x - 22$.