Question

Now, use this information to complete the equation for the line. Write it in slope-intercept form.

Answer 1

The equation of the line is $y=\frac{3}{2} x+4$.

Solution:

Given points are (2, 7) and (0, 4).

Slope of the line formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here $x_1=2, x_2=0, y_1=7, y_2=4$

Substitute these in the given formula.

$m=\frac{4-7}{0-2}$

   $=\frac{-3}{-2}$

$m=\frac{3}{2}$

Point-slope formula:

$y-y_1=m(x-x_1)$

You can take any point in the given line. Here the point is (2, 7).

$y-7=\frac{3}{2} (x-2)$

Multiply by 2 on both sides of the equation.

$2(y-7)=3(x-2)$

$2y-14=3x-6$

Add 14 on both sides of the equation.

$2y=3x+8$

Divide by 2 on both sides, we get

$y=\frac{3}{2} x+4$

The equation of the line is $y=\frac{3}{2} x+4$.