Question

constructed response
graph each equation. clearly mark at least three points on the line.

1. $y = -3x - 1$

1. $y = 2 - \frac{3}{4}x$

1. $x = 4$

1. $y = \frac{2}{3}(x - 21) + 8$

write the slope - intercept equation for each graph.
5.

equation: ____________
6.

equation: ____________

Explanation:

---

1. $y=-3x-1$

Step1: Pick x-values, solve for y

Choose $x=-1, 0, 1$:

• $x=-1$: $y=-3(-1)-1=2$ → $(-1,2)$
• $x=0$: $y=-3(0)-1=-1$ → $(0,-1)$
• $x=1$: $y=-3(1)-1=-4$ → $(1,-4)$

Step2: Plot points, draw line

Mark $(-1,2)$, $(0,-1)$, $(1,-4)$; connect them.

---

2. $y=2-\frac{3}{4}x$

Step1: Pick x-values, solve for y

Choose $x=0, 4, -4$:

• $x=0$: $y=2-\frac{3}{4}(0)=2$ → $(0,2)$
• $x=4$: $y=2-\frac{3}{4}(4)=-1$ → $(4,-1)$
• $x=-4$: $y=2-\frac{3}{4}(-4)=5$ → $(-4,5)$

Step2: Plot points, draw line

Mark $(0,2)$, $(4,-1)$, $(-4,5)$; connect them.

---

3. $x=4$

Step1: Identify line type, find points

Vertical line: all points have $x=4$.
Choose $y=-2, 0, 2$ → $(4,-2)$, $(4,0)$, $(4,2)$

Step2: Plot points, draw line

Mark $(4,-2)$, $(4,0)$, $(4,2)$; connect them.

---

4. $y=\frac{2}{3}(x-21)+8$

Step1: Simplify to slope-intercept form

$$\begin{align*} y&=\frac{2}{3}x - \frac{2}{3}(21)+8\\ y&=\frac{2}{3}x -14 +8\\ y&=\frac{2}{3}x -6 \end{align*}$$

Step2: Pick x-values, solve for y

Choose $x=0, 3, 6$:

• $x=0$: $y=\frac{2}{3}(0)-6=-6$ → $(0,-6)$
• $x=3$: $y=\frac{2}{3}(3)-6=-4$ → $(3,-4)$
• $x=6$: $y=\frac{2}{3}(6)-6=-2$ → $(6,-2)$

Step3: Plot points, draw line

Mark $(0,-6)$, $(3,-4)$, $(6,-2)$; connect them.

---

5. Graph to slope-intercept form

Step1: Identify intercepts and slope

Y-intercept: $(0,1)$; x-intercept: $(9,0)$
Slope $m=\frac{0-1}{9-0}=-\frac{1}{9}$

Step2: Write slope-intercept equation

$y=mx+b$ where $m=-\frac{1}{9}$, $b=1$
$$y=-\frac{1}{9}x +1$$

---

6. Graph to slope-intercept form

Step1: Identify points, calculate slope

Points: $(2,1)$, $(4,4)$
Slope $m=\frac{4-1}{4-2}=\frac{3}{2}$

Step2: Solve for y-intercept b

Use $(2,1)$: $1=\frac{3}{2}(2)+b$ → $1=3+b$ → $b=-2$

Step3: Write slope-intercept equation

$$y=\frac{3}{2}x -2$$

---

Answer:

1. Plotted points: $(-1,2)$, $(0,-1)$, $(1,-4)$; line connects these points
2. Plotted points: $(0,2)$, $(4,-1)$, $(-4,5)$; line connects these points
3. Plotted points: $(4,-2)$, $(4,0)$, $(4,2)$; vertical line connects these points
4. Plotted points: $(0,-6)$, $(3,-4)$, $(6,-2)$; line connects these points
5. $y=-\frac{1}{9}x +1$
6. $y=\frac{3}{2}x -2$