Answer:
[tex]7x - 4y = 42[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (6,0)[/tex]
[tex](x_2,y_2) = (2,-7)[/tex]
Required
Determine the equation in standard form
First, calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{-7 -0}{2 - 6}[/tex]
[tex]m = \frac{-7}{-4}[/tex]
[tex]m = \frac{7}{4}[/tex]
The equation in standard form is calculated using:
[tex]y - y_1 = m(x - x_1 )[/tex]
This gives:
[tex]y - 0 = \frac{7}{4}(x - 6)[/tex]
[tex]y = \frac{7}{4}(x - 6)[/tex]
Cross Multiply
[tex]4y = 7(x - 6)[/tex]
Open bracket
[tex]4y = 7x - 42[/tex]
Subtract 7x from both sides
[tex]-7x + 4y = 7x - 7x - 42[/tex]
[tex]-7x + 4y = - 42[/tex]
Multiply through by -1
[tex]-1(-7x + 4y) = - 42*-1[/tex]
[tex]7x - 4y = 42[/tex]
