Question

(given two points)
directions: write a linear equation that passes through the given two points.

1. (-4, -2) and (4, 0)
2. (3, 4) and (0, 5)
3. (0, 1) and (5, 3)
4. (2, -2) and (0, -1)
5. (0, 5) and (-5, 1)
6. (1, 3) and (-3, -5)
7. (1, 4) and (6, -1)
8. (3, 3) and (1, -3)
9. (-12, 14) and (6, -1)
10. (-1, 4) and (0, -1)

Explanation:

7. Step1: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{6-1}=\frac{-5}{5}=-1$

7. Step2: Find y-intercept $b$

Use point $(1,4)$: $4=-1(1)+b \implies b=5$

7. Step3: Write linear equation

$y=mx+b$
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8. Step1: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{1-3}=\frac{-6}{-2}=3$

8. Step2: Find y-intercept $b$

Use point $(3,3)$: $3=3(3)+b \implies b=3-9=-6$

8. Step3: Write linear equation

$y=mx+b$
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9. Step1: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-14}{6-(-12)}=\frac{-15}{18}=-\frac{5}{6}$

9. Step2: Find y-intercept $b$

Use point $(6,-1)$: $-1=-\frac{5}{6}(6)+b \implies -1=-5+b \implies b=4$

9. Step3: Write linear equation

$y=mx+b$
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10. Step1: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-1)}=\frac{-5}{1}=-5$

10. Step2: Find y-intercept $b$

Use point $(0,-1)$: $b=-1$

10. Step3: Write linear equation

$y=mx+b$

Answer:

1. $y=-x+5$
2. $y=3x-6$
3. $y=-\frac{5}{6}x+4$
4. $y=-5x-1$