Question

name: emily wong pd: date: 10/07/25 period: 4 topic 2 test study guide sections 2.1 - 2.4 due 10/9 section 2 - 1a: slope review find the slope using the graph or two points. simplify your answer. 1) (-2,3) and (-1,0) m = \\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{3 - 0}{-2-(-1)}=\frac{3}{-1}\\) m = - 3 2) (-1,-1) and (2,3) m = \\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1 - 3}{-1 - 2}=\frac{-4}{-3}\\) m = -\\(\frac{4}{3}\\) 3) (-4,13) and (6,-2) \\(x_{2}y_{2}\\) \\(x_{1}y_{1}\\) m = \\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{13-(-2)}{-4 - 6}=\frac{15}{-10}=-\frac{3}{2}\\) m = -\\(\frac{3}{2}\\) 4) (-2,4) and (10,-2) \\(x_{2}y_{2}\\) \\(x_{1}y_{1}\\) m = \\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{4-(-2)}{-2 - 10}=\frac{6}{-12}=-\frac{1}{2}\\) m = -\\(\frac{1}{2}\\) section 2 - 1b: slope - intercept form graph the linear equation in slope - intercept form. 5) y = \\(\frac{4}{5}x-1\\) m = \\(\frac{4}{5}\\), b = (-1) (0,-1) 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 point - pairs

1. For points $(-2,3)$ and $(-1,0)$:

• Substitute into formula: $m=\frac{3 - 0}{-2-(-1)}=\frac{3}{-1}=-3$.

1. For points $(-1,-1)$ and $(2,3)$:

• Substitute into formula: $m=\frac{-1 - 3}{-1 - 2}=\frac{-4}{-3}=\frac{4}{3}$.

1. For points $(-4,13)$ and $(6,-2)$:

• Substitute into formula: $m=\frac{13-(-2)}{-4 - 6}=\frac{15}{-10}=-\frac{3}{2}$.

1. For points $(-2,4)$ and $(10,-2)$:

• Substitute into formula: $m=\frac{4-(-2)}{-2 - 10}=\frac{6}{-12}=-\frac{1}{2}$.

Step3: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step4: Graph lines

1. For $y=\frac{4}{5}x-1$, $m = \frac{4}{5}$ and $b=-1$. Start at the y - intercept $(0, - 1)$ and use the slope $\frac{4}{5}$ (rise 4, run 5) to find another point and draw the line.
2. For $y=-3x + 6$, $m=-3$ and $b = 6$. Start at the y - intercept $(0,6)$ and use the slope $-3=\frac{-3}{1}$ (rise - 3, run 1) to find another point and draw the line.

Answer:

1. $m=-3$
2. $m=\frac{4}{3}$
3. $m=-\frac{3}{2}$
4. $m=-\frac{1}{2}$
5. Graph of $y=\frac{4}{5}x - 1$ with slope $\frac{4}{5}$ and y - intercept $(0,-1)$
6. Graph of $y=-3x + 6$ with slope $-3$ and y - intercept $(0,6)$