Writing Equations of Lines Given the Graph - Elementary Algebra Skill worksheet with eight line graphs on coordinate planes.

Let's solve each problem step by step. We are asked to write the slope-intercept form of the equation of each line shown in the graph.

The slope-intercept form is:

$$
y = mx + b
$$

Where:
- $ m $ is the slope of the line,
- $ b $ is the y-intercept (the point where the line crosses the y-axis).

We'll analyze each graph one by one.

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1)

Graph shows a line passing through points like $(-2, -4)$ and $(0, 0)$, and then going up to $(2, 4)$.

- Y-intercept ($b$): The line passes through the origin → $ b = 0 $
- Slope ($m$): Use two points: $(-2, -4)$ and $(2, 4)$
$$
m = \frac{4 - (-4)}{2 - (-2)} = \frac{8}{4} = 2
$$

✔ Equation:
$$
\boxed{y = 2x}
$$

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2)

Line goes from top-left to bottom-right, passing through $(-3, 4)$ and $(3, 0)$.

- Y-intercept: When $x = 0$, $y = 2$ → $ b = 2 $
- Slope: Use $(-3, 4)$ and $(3, 0)$
$$
m = \frac{0 - 4}{3 - (-3)} = \frac{-4}{6} = -\frac{2}{3}
$$

✔ Equation:
$$
\boxed{y = -\frac{2}{3}x + 2}
$$

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3)

Line slopes downward from left to right, passing through $(-4, 4)$ and $(0, 1)$.

- Y-intercept: At $x=0$, $y=1$ → $ b = 1 $
- Slope: Use $(-4, 4)$ and $(0, 1)$
$$
m = \frac{1 - 4}{0 - (-4)} = \frac{-3}{4} = -\frac{3}{4}
$$

✔ Equation:
$$
\boxed{y = -\frac{3}{4}x + 1}
$$

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4)

Horizontal line at $y = 3$

- Y-intercept: $ b = 3 $
- Slope: Horizontal lines have slope $ m = 0 $

✔ Equation:
$$
\boxed{y = 3}
$$

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5)

Line goes from $(-3, -2)$ to $(0, 2)$

- Y-intercept: At $x=0$, $y=2$ → $ b = 2 $
- Slope: Use $(-3, -2)$ and $(0, 2)$
$$
m = \frac{2 - (-2)}{0 - (-3)} = \frac{4}{3}
$$

✔ Equation:
$$
\boxed{y = \frac{4}{3}x + 2}
$$

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6)

Line passes through $(-2, -4)$ and $(1, 2)$

- Y-intercept: Let's find where it crosses $x=0$.
From $(-2, -4)$ to $(1, 2)$:
Slope: $ m = \frac{2 - (-4)}{1 - (-2)} = \frac{6}{3} = 2 $

Now use point-slope or plug into $y = 2x + b$:
Plug in $(1, 2)$:
$$
2 = 2(1) + b \Rightarrow b = 0
$$

✔ Equation:
$$
\boxed{y = 2x}
$$

Wait — check again: Does it pass through origin?

From graph: when $x = 0$, $y = 0$? Yes! It does.

So yes, $b = 0$

✔ Final: $ \boxed{y = 2x} $

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7)

Line passes through $(-2, -5)$ and $(0, 1)$

- Y-intercept: $x=0$, $y=1$ → $ b = 1 $
- Slope: $(-2, -5)$ to $(0, 1)$
$$
m = \frac{1 - (-5)}{0 - (-2)} = \frac{6}{2} = 3
$$

✔ Equation:
$$
\boxed{y = 3x + 1}
$$

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8)

Line passes through $(-3, -5)$ and $(0, 2)$

- Y-intercept: $x=0$, $y=2$ → $ b = 2 $
- Slope: $(-3, -5)$ to $(0, 2)$
$$
m = \frac{2 - (-5)}{0 - (-3)} = \frac{7}{3}
$$

✔ Equation:
$$
\boxed{y = \frac{7}{3}x + 2}
$$

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✔ Final Answers:

1) $ y = 2x $
2) $ y = -\frac{2}{3}x + 2 $
3) $ y = -\frac{3}{4}x + 1 $
4) $ y = 3 $
5) $ y = \frac{4}{3}x + 2 $
6) $ y = 2x $
7) $ y = 3x + 1 $
8) $ y = \frac{7}{3}x + 2 $

Let me know if you'd like these verified with graphs or need help plotting them!