Answer:
[tex]y= -\frac{2}{3}x + 12[/tex] --- (1)
[tex]y = -2x -6[/tex] --- (2)
Step-by-step explanation:
Solving (a): Line Equation
[tex](x_1,y_1) = (3,10)[/tex]
[tex](x_2,y_2) = (6,8)[/tex]
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8 - 10}{6 -3}[/tex]
[tex]m = \frac{-2}{3}[/tex]
[tex]m = -\frac{2}{3}[/tex]
The line equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex] --- slope intercept formula
This gives:
[tex]y - 10 = -\frac{2}{3}(x - 3)[/tex]
[tex]y - 10 = -\frac{2}{3}x + 2[/tex]
Solve for y
[tex]y= -\frac{2}{3}x + 2+10[/tex]
[tex]y= -\frac{2}{3}x + 12[/tex]
Solving (b): Line Equation
[tex](x_1,y_1) = (2,-10)[/tex]
[tex](x_2,y_2) = (-4,2)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 -(- 10)}{-4 -2}[/tex]
[tex]m = \frac{2 + 10}{-6}[/tex]
[tex]m = \frac{12}{-6}[/tex]
[tex]m=-2[/tex]
The line equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-10) = -2(x - 2)[/tex]
[tex]y +10 = -2(x - 2)[/tex]
[tex]y +10 = -2x +4[/tex]
Solve for y
[tex]y = -2x +4-10[/tex]
[tex]y = -2x -6[/tex]
