Question

state the slope and the y-int. for each, then graph the line. include at least 3 points on each line.

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

$m = \underline{\quad\quad\quad}, b = \underline{\quad\quad\quad}$

1. $y = 2x - 5$

slope = $\underline{\quad\quad\quad}$, y-int. = $\underline{\quad\quad\quad}$

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

$m = \underline{\quad\quad\quad}, b = \underline{\quad\quad\quad}$

1. $y = -\frac{5}{3}x$

slope = $\underline{\quad\quad\quad}$, y-int. = $\underline{\quad\quad\quad}$

Explanation:

For Problem 4: $y = \frac{1}{3}x + 4$

Step1: Identify slope ($m$)

The equation is in slope-intercept form $y=mx+b$, so $m = \frac{1}{3}$.

Step2: Identify y-intercept ($b$)

From $y=mx+b$, $b = 4$ (point $(0,4)$).

Step3: Find 2 more points

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

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For Problem 5: $y = 2x - 5$

Step1: Identify slope

From $y=mx+b$, slope $= 2$.

Step2: Identify y-intercept

From $y=mx+b$, y-int. $= -5$ (point $(0,-5)$).

Step3: Find 2 more points

• Let $x=3$: $y = 2(3) - 5 = 1$ → $(3,1)$
• Let $x=1$: $y = 2(1) - 5 = -3$ → $(1,-3)$

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For Problem 6: $y = -\frac{1}{2}x + 3$

Step1: Identify slope ($m$)

From $y=mx+b$, $m = -\frac{1}{2}$.

Step2: Identify y-intercept ($b$)

From $y=mx+b$, $b = 3$ (point $(0,3)$).

Step3: Find 2 more points

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

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For Problem 7: $y = -\frac{5}{3}x$

Step1: Identify slope

From $y=mx+b$, slope $= -\frac{5}{3}$.

Step2: Identify y-intercept

From $y=mx+b$, $b=0$ (y-int. $= 0$, point $(0,0)$).

Step3: Find 2 more points

• Let $x=3$: $y = -\frac{5}{3}(3) = -5$ → $(3,-5)$
• Let $x=-3$: $y = -\frac{5}{3}(-3) = 5$ → $(-3,5)$

Answer:

Problem 4:

Slope ($m$) = $\frac{1}{3}$, Y-intercept ($b$) = $4$
Points to graph: $(0,4)$, $(3,5)$, $(-3,3)$

Problem 5:

Slope = $2$, Y-intercept = $-5$
Points to graph: $(0,-5)$, $(3,1)$, $(1,-3)$

Problem 6:

Slope ($m$) = $-\frac{1}{2}$, Y-intercept ($b$) = $3$
Points to graph: $(0,3)$, $(2,2)$, $(-2,4)$

Problem 7:

Slope = $-\frac{5}{3}$, Y-intercept = $0$
Points to graph: $(0,0)$, $(3,-5)$, $(-3,5)$

(To graph each line: plot the three points for each equation, then draw a straight line connecting them across the coordinate grid.)