Question

writing linear equations from graphs practice
directions: for each graph below, find the slope and y-intercept simplify the slope, if needed.
use those to write the equation in slope-intercept form in the dotted box.
1)
slope
y-int
equation:
2)
slope
y-int
equation:
3)
slope
y-int
equation:
4)
slope
y-int
equation:
5)
slope
y-int
equation:
6)
slope
y-int
equation:
7)
slope
y-int
equation:
8)
slope
y-int
equation:

Explanation:

1)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -1)$, so $b=-1$.

Step2: Calculate slope

Use two points $(0, -1)$ and $(6, 0)$. Slope $m=\frac{0-(-1)}{6-0}=\frac{1}{6}$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{6}$ and $b=-1$.
$y=\frac{1}{6}x - 1$

2)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 14)$, so $b=14$.

Step2: Calculate slope

Use two points $(0, 14)$ and $(5, 0)$. Slope $m=\frac{0-14}{5-0}=-\frac{14}{5}$

Step3: Write slope-intercept form

Substitute $m=-\frac{14}{5}$ and $b=14$.
$y=-\frac{14}{5}x + 14$

3)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$.

Step2: Calculate slope

Use two points $(0, 3)$ and $(6, 8)$. Slope $m=\frac{8-3}{6-0}=\frac{5}{6}$

Step3: Write slope-intercept form

Substitute $m=\frac{5}{6}$ and $b=3$.
$y=\frac{5}{6}x + 3$

4)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 1)$, so $b=1$.

Step2: Calculate slope

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

Step3: Write slope-intercept form

Substitute $m=\frac{1}{2}$ and $b=1$.
$y=\frac{1}{2}x + 1$

5)

Step1: Identify line type

This is a vertical line at $x=0$ (the y-axis). Vertical lines have undefined slope, and no y-intercept (it is the y-axis).

Step2: Write equation

Vertical line equation: $x=0$

6)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 0)$, so $b=0$.

Step2: Calculate slope

Use two points $(0, 0)$ and $(2, 9)$. Slope $m=\frac{9-0}{2-0}=\frac{9}{2}$

Step3: Write slope-intercept form

Substitute $m=\frac{9}{2}$ and $b=0$.
$y=\frac{9}{2}x$

7)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 2)$, so $b=2$.

Step2: Calculate slope

Use two points $(0, 2)$ and $(2, -1)$. Slope $m=\frac{-1-2}{2-0}=-\frac{3}{2}$

Step3: Write slope-intercept form

Substitute $m=-\frac{3}{2}$ and $b=2$.
$y=-\frac{3}{2}x + 2$

8)

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -3)$, so $b=-3$.

Step2: Calculate slope

Horizontal line has slope $m=0$.

Step3: Write slope-intercept form

Substitute $m=0$ and $b=-3$.
$y=-3$

Answer:

1. Slope: $\frac{1}{6}$, y-int: $-1$, Equation: $y=\frac{1}{6}x - 1$
2. Slope: $-\frac{14}{5}$, y-int: $14$, Equation: $y=-\frac{14}{5}x + 14$
3. Slope: $\frac{5}{6}$, y-int: $3$, Equation: $y=\frac{5}{6}x + 3$
4. Slope: $\frac{1}{2}$, y-int: $1$, Equation: $y=\frac{1}{2}x + 1$
5. Slope: Undefined, y-int: None, Equation: $x=0$
6. Slope: $\frac{9}{2}$, y-int: $0$, Equation: $y=\frac{9}{2}x$
7. Slope: $-\frac{3}{2}$, y-int: $2$, Equation: $y=-\frac{3}{2}x + 2$
8. Slope: $0$, y-int: $-3$, Equation: $y=-3$