Question - Graphing a Line in Slope-Intercept Form
Solution:
Based on the image provided, the equation of the line is $$y + 3 = \frac{9}{4}(x + 4)$$. To graph this line, it's typically easiest to write it in slope-intercept form, which is $$y = mx + b$$, where $$m$$ is the slope of the line and $$b$$ is the y-intercept.Let's rewrite the given equation in slope-intercept form:$$\begin{align*}y + 3 &= \frac{9}{4}(x + 4) \\y &= \frac{9}{4}x + \frac{9}{4} \cdot 4 - 3 \\y &= \frac{9}{4}x + 9 - 3 \\y &= \frac{9}{4}x + 6\end{align*}$$Now we have the equation in slope-intercept form, with a slope $$m=\frac{9}{4}$$ and a y-intercept $$b=6$$.To graph this line:1. Start at the y-intercept (0,6) on the graph.2. Use the slope to find another point. The slope is the rise over the run, meaning you go up 9 units and right 4 units from the y-intercept (or down 9 and left 4, for a point in the opposite direction).3. Plot the second point.4. Draw a line through the two points, extending it across the graph.This straight line represents the equation $$y = \frac{9}{4}x + 6$$.
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