The equation of the line is [tex]y=\frac{3}{2} x+4[/tex].
Solution:
Given points are (2, 7) and (0, 4).
Slope of the line formula:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here [tex]x_1=2, x_2=0, y_1=7, y_2=4[/tex]
Substitute these in the given formula.
[tex]$m=\frac{4-7}{0-2}[/tex]
[tex]$=\frac{-3}{-2}[/tex]
[tex]$m=\frac{3}{2}[/tex]
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
You can take any point in the given line. Here the point is (2, 7).
[tex]$y-7=\frac{3}{2} (x-2)[/tex]
Multiply by 2 on both sides of the equation.
[tex]2(y-7)=3(x-2)[/tex]
[tex]2y-14=3x-6[/tex]
Add 14 on both sides of the equation.
[tex]2y=3x+8[/tex]
Divide by 2 on both sides, we get
[tex]$y=\frac{3}{2} x+4[/tex]
The equation of the line is [tex]y=\frac{3}{2} x+4[/tex].
