Question

graph the equation.

1. $y - 6 = 3(x - 4)$
2. $y + 1 = 2(x - 5)$
3. $y - 2 = -4(x + 3)$
4. $y + 2 = -(x - 1)$
5. $y = \frac{1}{2}(x - 5)$
6. $y + 3 = 5x$
7. $y + 1 = \frac{2}{3}(x + 1)$
8. $y - 2 = -\frac{1}{2}(x - 3)$
9. $y + \frac{1}{2} = 2(x - 1)$

Explanation:

All equations are in point-slope form $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line, and $m$ is the slope ($\frac{\text{rise}}{\text{run}}$). We use this to graph each line.

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Problem 11: $y + 1 = 2(x - 5)$

Step1: Identify point and slope

Point: $(5, -1)$, Slope $m=2=\frac{2}{1}$

Step2: Plot point, use slope

From $(5,-1)$, rise 2, run 1 to $(6,1)$; draw line.

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Problem 13: $y + 2 = -(x - 1)$

Step1: Identify point and slope

Point: $(1, -2)$, Slope $m=-1=\frac{-1}{1}$

Step2: Plot point, use slope

From $(1,-2)$, rise -1, run 1 to $(2,-3)$; draw line.

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Problem 14: $y = \frac{1}{2}(x - 5)$

Step1: Identify point and slope

Point: $(5, 0)$, Slope $m=\frac{1}{2}$

Step2: Plot point, use slope

From $(5,0)$, rise 1, run 2 to $(7,1)$; draw line.

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Problem 15: $y + 3 = 5x$ (rewrite as $y+3=5(x-0)$)

Step1: Identify point and slope

Point: $(0, -3)$, Slope $m=5=\frac{5}{1}$

Step2: Plot point, use slope

From $(0,-3)$, rise 5, run 1 to $(1,2)$; draw line.

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Problem 16: $y + 1 = \frac{2}{3}(x + 1)$

Step1: Identify point and slope

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

Step2: Plot point, use slope

From $(-1,-1)$, rise 2, run 3 to $(2,1)$; draw line.

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Problem 17: $y - 2 = -\frac{1}{2}(x - 3)$

Step1: Identify point and slope

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

Step2: Plot point, use slope

From $(3,2)$, rise -1, run 2 to $(5,1)$; draw line.

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Problem 18: $y + \frac{1}{2} = 2(x - 1)$

Step1: Identify point and slope

Point: $(1, -\frac{1}{2})$, Slope $m=2=\frac{2}{1}$

Step2: Plot point, use slope

From $(1,-\frac{1}{2})$, rise 2, run 1 to $(2,\frac{3}{2})$; draw line.

Answer:

1. Line passes through $(5,-1)$ with slope 2.
2. Line passes through $(1,-2)$ with slope -1.
3. Line passes through $(5,0)$ with slope $\frac{1}{2}$.
4. Line passes through $(0,-3)$ with slope 5.
5. Line passes through $(-1,-1)$ with slope $\frac{2}{3}$.
6. Line passes through $(3,2)$ with slope $-\frac{1}{2}$.
7. Line passes through $(1,-\frac{1}{2})$ with slope 2.

(Note: For each problem, the graph is a straight line connecting the identified points and extended across the grid.)