Question

14. Write the equation using the slope-intercept form.

Answer 1

Given:

We need to determine the equation of the line using the slope - intercept form.

(14) Equation of the line:

The slope of the line is $m=-\frac{2}{3}$ and the y - intercept is $b=9$

The equation of the line can be determined using the formula,

$y=mx+b$

Substituting the values, we get;

$y=-\frac{2}{3}x+9$

Therefore, the equation of the line is $y=-\frac{2}{3}x+9$

(15) Equation of the line:

The slope of the line is $m=3$ and the point (2,-9)

The equation of the line can be determined using the formula,

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

Substituting the values, we get;

$y+9=3(x-2)$

$y+9=3x-6$

     $y=3x-15$

Thus, the equation of the line is $y=3x-15$

(16) Equation of the line:

The two points of the line are (9,8) and (-6,-2)

The slope of the line is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-2-8}{-6-9}$

$m=\frac{-10}{-15}$

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

The equation of the line can be determined using the formula,

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

Substituting the values, we get;

$y-8=\frac{2}{3}(x-9)$

$y-8=\frac{2}{3}x-6$

     $y=\frac{2}{3}x+2$

Thus, the equation of the line is $y=\frac{2}{3}x+2$