Question

1. graph the line through (1,2) with a slope of $\frac{3}{5}$.

Explanation:

Step1: Recall the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Here, $x_1 = 1$, $y_1=2$ and $m=\frac{3}{5}$.

Step2: Substitute the values into the point - slope form

Substituting gives $y - 2=\frac{3}{5}(x - 1)$.

Step3: Find another point on the line

We can find another point by using the slope. The slope $m=\frac{3}{5}=\frac{\Delta y}{\Delta x}$. Starting from the point $(1,2)$, if we move $\Delta x = 5$ units to the right (increase $x$ by 5), then $\Delta y=3$ (increase $y$ by 3). So another point is $(1 + 5,2+3)=(6,5)$.

Step4: Graph the line

Plot the points $(1,2)$ and $(6,5)$ on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points $(1,2)$ and $(6,5)$ and draw a line through them.