To obtain the slope of a line given two points, use the formula below
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In our case,
[tex]m=\frac{3-(-1)}{4-0}=\frac{4}{4}=1[/tex]
Then, in general, the slope-intercept form of the equation of a line is
[tex]\begin{gathered} y=mx+b \\ m\rightarrow\text{ slope} \\ b\rightarrow\text{ y-intercept} \end{gathered}[/tex]
Thus, in our case,
[tex]\begin{gathered} \Rightarrow y=1*x+(-1)=x-1 \\ \Rightarrow y=x-1 \end{gathered}[/tex]
a) The equation of the line is y=x-1. To graph it, draw (4,3) and (0,-1) on the plane; then, cross them using a line, as shown below
b) Set y=0 in the equation we found in part a); then, solve for x, as shown below
[tex]\begin{gathered} y=0 \\ \Rightarrow0=x-1 \\ \Rightarrow x=1 \\ \Rightarrow(1,0) \end{gathered}[/tex]
The x-intercept of the line is (1,0)
