Respuesta :
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 [tex]m=-\frac{2}{3}[/tex] and the y - intercept is [tex]b=9[/tex]
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we get;
[tex]y=-\frac{2}{3}x+9[/tex]
Therefore, the equation of the line is [tex]y=-\frac{2}{3}x+9[/tex]
(15) Equation of the line:
The slope of the line is [tex]m=3[/tex] and the point (2,-9)
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the values, we get;
[tex]y+9=3(x-2)[/tex]
[tex]y+9=3x-6[/tex]
[tex]y=3x-15[/tex]
Thus, the equation of the line is [tex]y=3x-15[/tex]
(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
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-8}{-6-9}[/tex]
[tex]m=\frac{-10}{-15}[/tex]
[tex]m=\frac{2}{3}[/tex]
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the values, we get;
[tex]y-8=\frac{2}{3}(x-9)[/tex]
[tex]y-8=\frac{2}{3}x-6[/tex]
[tex]y=\frac{2}{3}x+2[/tex]
Thus, the equation of the line is [tex]y=\frac{2}{3}x+2[/tex]
