Use the image to answer the question.

Question

A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 8 comma 0 right parenthesis, left parenthesis 0 comma 4 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.

Find the slope of the line given its graph.

(1 point)
Responses

−12
negative Start Fraction 1 over 2 End Fraction

2
2

12
Start Fraction 1 over 2 End Fraction

4
4
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Answer 1

To find the slope of the line connecting the points \((-8, 0)\) and \((0, 4)\), we can use the slope formula:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, the points \((-8, 0)\) and \((0, 4)\) give us:

• \((x_1, y_1) = (-8, 0)\)
• \((x_2, y_2) = (0, 4)\)

Substituting these values into the formula:

\[ m = \frac{4 - 0}{0 - (-8)} = \frac{4}{0 + 8} = \frac{4}{8} = \frac{1}{2} \]

Thus, the slope of the line is \(\frac{1}{2}\).

The correct response from the given options is:

Start Fraction 1 over 2 End Fraction