To find the equation of the line in slope-intercept form (y = mx + b), we need the slope (m) and the y-intercept (b).
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Calculate the slope (m) using the two points (-4, -5) and (4, 5):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4} \]
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Use one of the points to find the y-intercept (b). Let's use the point (4, 5):
We know the line has the form \(y = mx + b\). Plugging in \(m = \frac{5}{4}\) and the point (4, 5):
\[ 5 = \frac{5}{4}(4) + b \] \[ 5 = 5 + b \] \[ b = 5 - 5 = 0 \]
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Write the equation in slope-intercept form:
Now that we have the slope and the y-intercept, we can write the equation:
\[ y = \frac{5}{4}x + 0 \]
This simplifies to:
\[ y = \frac{5}{4}x \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{5}{4}x \]
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