Question

name: emily wong paz date: 10/07/25 period: 4 topic 2 test study guide: sections 2.1 - 2.4 section 2 - 1a: slope review find the slope using the graph or two points. simplify your answer. 1) (-2,3) and (-1,0) 2) (-1,-3) and (2,3) 3) (-4,13) and (6,-2) 4) (-2,4) and (10,-2) section 2 - 1b: slope - intercept form graph the linear equation in slope - intercept form. 6) y = - 3x + 6 m=-3, b = 6 (0,6)

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope for $(-4,13)$ and $(6,-2)$

Let $(x_1,y_1)=(-4,13)$ and $(x_2,y_2)=(6,-2)$. Then $m=\frac{-2 - 13}{6-(-4)}=\frac{-15}{10}=-\frac{3}{2}$.

Step3: Calculate slope for $(-2,-2)$ and $(10,4)$

Let $(x_1,y_1)=(-2,-2)$ and $(x_2,y_2)=(10,4)$. Then $m=\frac{4-(-2)}{10 - (-2)}=\frac{6}{12}=\frac{1}{2}$.

Step4: Analyze slope - intercept form

For the equation $y=-3x + 6$, the slope $m=-3$ and the y - intercept $b = 6$. To graph it, start at the y - intercept $(0,6)$ and use the slope. Since $m=-3=\frac{-3}{1}$, from the point $(0,6)$ move 1 unit to the right and 3 units down to find another point on the line.

Answer:

For the points $(-4,13)$ and $(6,-2)$, the slope is $-\frac{3}{2}$. For the points $(-2,-2)$ and $(10,4)$, the slope is $\frac{1}{2}$. The graph of $y=-3x + 6$ has a y - intercept at $(0,6)$ and a slope of $-3$.