To find the equation of a line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).
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Find the slope (m): The slope is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (-3, 0) and (0, 4):
Let \((x_1, y_1) = (-3, 0)\) and \((x_2, y_2) = (0, 4)\).
\[ m = \frac{4 - 0}{0 - (-3)} = \frac{4}{3} \]
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Find the y-intercept (b): The y-intercept is the value of y when x = 0. From the second point (0, 4), we can see that the y-intercept \(b = 4\).
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Write the equation in slope-intercept form: Now that we have the slope and y-intercept, we can write the equation of the line:
\[ y = \frac{4}{3}x + 4 \]
So, the equation of the line in slope-intercept form is:
\[ y = \frac{4}{3}x + 4 \]