Question

unit 4: linear equations
bell: 3rd
homework 7: writing linear equations (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)

Explanation:

Step1: Calculate slope for Q3

Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(5,3)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{5-0}=\frac{2}{5}$

Step2: Find y-intercept for Q3

Use $(0,1)$: $b=1$. Substitute into $y=mx+b$.
Equation: $y=\frac{2}{5}x+1$

Step3: Calculate slope for Q4

Let $(x_1,y_1)=(2,-2)$ and $(x_2,y_2)=(0,-1)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-2)}{0-2}=\frac{1}{-2}=-\frac{1}{2}$

Step4: Find y-intercept for Q4

Use $(0,-1)$: $b=-1$. Substitute into $y=mx+b$.
Equation: $y=-\frac{1}{2}x-1$

Step5: Calculate slope for Q5

Let $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(-5,1)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-5}{-5-0}=\frac{-4}{-5}=\frac{4}{5}$

Step6: Find y-intercept for Q5

Use $(0,5)$: $b=5$. Substitute into $y=mx+b$.
Equation: $y=\frac{4}{5}x+5$

Step7: Calculate slope for Q6

Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(-3,-5)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-3}{-3-1}=\frac{-8}{-4}=2$

Step8: Find y-intercept for Q6

Substitute $(1,3)$ and $m=2$ into $y=mx+b$:
$3=2(1)+b \implies b=1$. Equation: $y=2x+1$

Answer:

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