Question

1. (6, 8) and (2, 5); m = ____ b=____

equation= _______________

1. (2, 4) and (3, 6); m = ____ b=____

equation= _______________

1. (4, 1) and (8, 2); m = ____ b=____

equation= _______________

1. (-1, 1) and (1, 5); m = ____ b=____

equation= _______________

1. (-2, 3) and (2, 7); m = ____ b=____

equation= _______________

1. (-9, 5) and (-3, 3); m = ____ b=____

equation= _______________

Explanation:

Problem 11) (2, 4) and (3, 6)

Step1: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-4}{3-2}=2$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $(2,4)$: $4=2(2)+b \implies b=0$

Step3: Write equation

$y=2x$

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Problem 12) (-2, 3) and (2, 7)

Step1: Calculate slope $m$

$m=\frac{7-3}{2-(-2)}=\frac{4}{4}=1$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $(-2,3)$: $3=1(-2)+b \implies b=5$

Step3: Write equation

$y=x+5$

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Problem 14) (4, 1) and (8, 2)

Step1: Calculate slope $m$

$m=\frac{2-1}{8-4}=\frac{1}{4}$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $(4,1)$: $1=\frac{1}{4}(4)+b \implies b=0$

Step3: Write equation

$y=\frac{1}{4}x$

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Problem 15) (-9, 5) and (-3, 3)

Step1: Calculate slope $m$

$m=\frac{3-5}{-3-(-9)}=\frac{-2}{6}=-\frac{1}{3}$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $(-9,5)$: $5=-\frac{1}{3}(-9)+b \implies 5=3+b \implies b=2$

Step3: Write equation

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

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Answer:

11)

$m=2$, $b=0$
Equation: $y=2x$

12)

$m=1$, $b=5$
Equation: $y=x+5$

14)

$m=\frac{1}{4}$, $b=0$
Equation: $y=\frac{1}{4}x$

15)

$m=-\frac{1}{3}$, $b=2$
Equation: $y=-\frac{1}{3}x+2$

(Note: Problems 9 and 8 are partially cut off and cannot be solved from the provided image)