Question

graph the line with slope $\frac{1}{3}$ passing through the point $(-3,5)$.

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Given $m=\frac{1}{3}$ and $(x_1,y_1)=(-3,5)$, we have $y - 5=\frac{1}{3}(x + 3)$.

Step2: Simplify the equation

Expand the right - hand side: $y-5=\frac{1}{3}x + 1$. Then add 5 to both sides to get the slope - intercept form $y=\frac{1}{3}x+6$.

Step3: Find another point

Let $x = 0$, then $y=\frac{1}{3}(0)+6 = 6$, so we have the point $(0,6)$.

Step4: Graph the line

Plot the points $(-3,5)$ and $(0,6)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Graph the line by plotting the points $(-3,5)$ and $(0,6)$ and drawing a straight line through them.