Given that the line passes through the two points (-3,4) and (2,8)
We need to determine the equation of the line.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,4) and (2,8) in the above formula, we get;
[tex]m=\frac{8-4}{2+3}[/tex]
[tex]m=\frac{4}{5}[/tex]
Thus, the slope of the line is [tex]m=\frac{4}{5}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (-3,4) and [tex]m=\frac{4}{5}[/tex] in the above formula, we have;
[tex]y-4=\frac{4}{5}(x+3)[/tex]
[tex]y-4=\frac{4}{5}x+\frac{12}{5}[/tex]
[tex]y=\frac{4}{5}x+\frac{12}{5}+4[/tex]
[tex]y=\frac{4}{5}x+\frac{32}{5}[/tex]
Thus, the equation of the line is [tex]y=\frac{4}{5}x+\frac{32}{5}[/tex]
