Question - Graphing Equations in Slope-Intercept Form
Solution:
To graph the equation $$ y + 6 = -\frac{3}{4}(x + 3) $$, you should first rewrite it in slope-intercept form, which is $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept.Starting with the given equation:$$ y + 6 = -\frac{3}{4}(x + 3) $$Isolate $$ y $$ on one side of the equation:$$ y = -\frac{3}{4}(x + 3) - 6 $$Now distribute $$ -\frac{3}{4} $$ to both terms inside the parentheses:$$ y = -\frac{3}{4}x - \frac{3}{4} \cdot 3 - 6 $$Multiply $$ -\frac{3}{4} $$ by 3 to get $$ -\frac{9}{4} $$, and then continue to simplify:$$ y = -\frac{3}{4}x - \frac{9}{4} - 6 $$Since $$ 6 = \frac{24}{4} $$, we have:$$ y = -\frac{3}{4}x - \frac{9}{4} - \frac{24}{4} $$Combine the constant terms:$$ y = -\frac{3}{4}x - \frac{33}{4} $$So the equation in slope-intercept form is:$$ y = -\frac{3}{4}x - \frac{33}{4} $$Now you can graph the line with the slope $$ -\frac{3}{4} $$ and a y-intercept $$ -\frac{33}{4} $$. Start by plotting the y-intercept on the y-axis at the point (0, -$$ \frac{33}{4} $$) or (0, -8.25). Then, use the slope to find another point. From the y-intercept, move 3 units down and 4 units to the right (since the slope is negative), which will give you another point on the line. Connect these points with a straight line, and you will have graphed the given equation.
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