Question

1. write the equation of the line below in slope-intercept form.

Explanation:

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<reasoning>

Identify the y-intercept

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &\text{The line crosses the } y\text{-axis at } (0, -7).\\ &b = -7 \end{aligned}$$

\]

Determine the slope

Using the Slope of a Line knowledge point
\[

$$\begin{aligned} &\text{Identify two points on the line: } (0, -7) \text{ and } (4, 1).\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-7)}{4 - 0} = \frac{8}{4} = 2 \end{aligned}$$

\]

Write the equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = 2x - 7 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 2x - 7\)
</answer>

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Answer:

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<reasoning>

Identify the y-intercept

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &\text{The line crosses the } y\text{-axis at } (0, -7).\\ &b = -7 \end{aligned}$$

\]

Determine the slope

Using the Slope of a Line knowledge point
\[

$$\begin{aligned} &\text{Identify two points on the line: } (0, -7) \text{ and } (4, 1).\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-7)}{4 - 0} = \frac{8}{4} = 2 \end{aligned}$$

\]

Write the equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = 2x - 7 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 2x - 7\)
</answer>

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