graph this line: y + 6 = \\frac{3}{4}(x + 10) click to select points on the graph.

Explanation:

Step1: Rewrite in slope - intercept form

First, distribute the $\frac{3}{4}$ on the right - hand side: $y + 6=\frac{3}{4}x+\frac{3}{4}\times10=\frac{3}{4}x+\frac{15}{2}$. Then, subtract 6 from both sides to get $y=\frac{3}{4}x+\frac{15}{2}-6$. Since $6=\frac{12}{2}$, we have $y=\frac{3}{4}x+\frac{15 - 12}{2}=\frac{3}{4}x+\frac{3}{2}$.

Step2: Find the y - intercept

The y - intercept is the value of y when x = 0. Substitute x = 0 into $y=\frac{3}{4}x+\frac{3}{2}$, we get $y=\frac{3}{2}=1.5$. So the y - intercept is the point $(0,1.5)$.

Step3: Find another point using the slope

The slope $m = \frac{3}{4}$. Starting from the y - intercept $(0,1.5)$, if we move 4 units to the right (increase x by 4), then we move 3 units up (increase y by 3) according to the slope. So another point is $(4,1.5 + 3)=(4,4.5)$.

Step4: Graph the line

Plot the points $(0,1.5)$ and $(4,4.5)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points $(0,1.5)$ and $(4,4.5)$ and draw a line through them.