Step 1: Write out the formula for finding the slope m of a line given two points (x₁ y₁) and (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Pick any two points on the first line and substitute the value of into the formula to find the slope
The points (0, 0) and (1, 3) are on the first line.
Therefore, we can set
[tex]\begin{gathered} (x_1,y_1)=(0,0)\text{ and} \\ (x_2,y_2)=(1,3) \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x_1=0, \\ y_1=0 \\ x_2=1, \\ y_2=3 \end{gathered}[/tex]Therefore,
[tex]m=\frac{3-0}{1-0}=\frac{3}{1}=3[/tex]Hence, the slope of the first line is 3
Step 3: Pick any two points on the second line and substitute the value of into the formula to find the slope
The points (0, 3) and (4, 2) are on the first line.
Therefore, we can set
[tex]\begin{gathered} (x_1,y_1)=(0,3)\text{ and} \\ (x_2,y_2)=(4,2) \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x_1=0, \\ y_1=3 \\ x_2=4, \\ y_2=2 \end{gathered}[/tex]Therefore,
[tex]m=\frac{2-3}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]Hence, the slope of the second line is -1/4