Question

lesson 5.1
write an equation of the line shown.
4.
5.
6.
7.
8.
9.

Explanation:

We use the slope-intercept form $y=mx+b$, where $m$ is slope ($m=\frac{y_2-y_1}{x_2-x_1}$) and $b$ is the y-intercept (where $x=0$).

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Problem 4

Step1: Identify y-intercept $b$

The line crosses $(0,3)$, so $b=3$.

Step2: Calculate slope $m$

Use points $(0,3)$ and $(2,4)$:
$m=\frac{4-3}{2-0}=\frac{1}{2}$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=\frac{1}{2}x+3$

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Problem 5

Step1: Identify y-intercept $b$

The line crosses $(0,-3)$, so $b=-3$.

Step2: Calculate slope $m$

Use points $(0,-3)$ and $(-3,1)$:
$m=\frac{1-(-3)}{-3-0}=\frac{4}{-3}=-\frac{4}{3}$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=-\frac{4}{3}x-3$

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Problem 6

Step1: Identify y-intercept $b$

The line crosses $(0,4)$, so $b=4$.

Step2: Calculate slope $m$

Use points $(0,4)$ and $(-3,2)$:
$m=\frac{2-4}{-3-0}=\frac{-2}{-3}=\frac{2}{3}$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=\frac{2}{3}x+4$

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Problem 7

Step1: Identify y-intercept $b$

The line crosses $(0,-2)$, so $b=-2$.

Step2: Calculate slope $m$

Use points $(0,-2)$ and $(2,4)$:
$m=\frac{4-(-2)}{2-0}=\frac{6}{2}=3$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=3x-2$

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Problem 8

Step1: Identify y-intercept $b$

Use points $(-1,5)$ and $(1,-3)$ to solve for $b$. First find $m$:
$m=\frac{-3-5}{1-(-1)}=\frac{-8}{2}=-4$

Step2: Solve for $b$

Substitute $(-1,5)$ and $m=-4$ into $y=mx+b$:
$5=-4(-1)+b \implies 5=4+b \implies b=1$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=-4x+1$

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Problem 9

Step1: Identify y-intercept $b$

The line crosses $(0,4)$, so $b=4$.

Step2: Calculate slope $m$

Use points $(0,4)$ and $(-1,-1)$:
$m=\frac{-1-4}{-1-0}=\frac{-5}{-1}=5$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y=5x+4$

Answer:

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