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: Calculate 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 $y - y_1 = m(x - x_1)$ with $m=-8$ and the point $(-4,10)$. So $y - 10=-8(x + 4)$. Expand it: $y-10=-8x - 32$. Add 10 to both sides: $y=-8x - 22$. The y - intercept $b$ is - 22.

Step3: Write the equation of the line

Using the slope - intercept form $y = mx + b$, with $m=-8$ and $b = - 22$, the equation is $y=-8x - 22$.

Part (a)

Answer:

The slope of the line is -8.

Part (b)