The form of the linear equation is
[tex]y=mx+b[/tex]
m is the slope of the line of the equation
b is the y-intercept (value of y at x = 0)
The rule of the slope of the line which passes through points (x1, y1) and (x2, y2) is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Since the line passes through points (-3, 1) and (4, 8), then
Let (x1, y1) = (-3, 1) and (x2, y2) = (4, 8), then
[tex]\begin{gathered} x_{_1}=-3,x_2=4 \\ y_1=1,y_2=8 \end{gathered}[/tex]
Substitute them in the rule of m above
[tex]\begin{gathered} m=\frac{8-1}{4-(-3)} \\ m=\frac{7}{4+3} \\ m=\frac{7}{7} \\ m=1 \end{gathered}[/tex]
Now, substitute m by 1 in the form of the equation
[tex]\begin{gathered} y=(1)x+b \\ y=x+b \end{gathered}[/tex]
We need to find the value of b, to do that we will use the point (4, 8)
Substitute x by 4 and y by 2 in the equation
[tex]\begin{gathered} x=4,y=8 \\ 8=4+b \end{gathered}[/tex]
Subtract 4 from both sides to find b
[tex]\begin{gathered} 8-4=4-4+b \\ 4=b \end{gathered}[/tex]
Substitute b by 4 in the equation
[tex]y=x+4[/tex]
The equation of the line is y = x + 4
Answer B
