Answer:
[tex]y = -7x + 22[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (4,-6)[/tex]
[tex](x_2,y_2) = (2,8)[/tex]
Required
Determine the line equation
This question will be answered using linear interpolation.
This is represented as thus:
[tex]\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substitute values for x1,x2,y1 and y2
[tex]\frac{y - (-6)}{x - 4} = \frac{8 - (-6)}{2 - 4}[/tex]
[tex]\frac{y +6}{x - 4} = \frac{8 +6}{2 - 4}[/tex]
[tex]\frac{y +6}{x - 4} = \frac{14}{-2}[/tex]
[tex]\frac{y +6}{x - 4} =-7[/tex]
Cross Multiply
[tex]y + 6 = -7(x - 4)[/tex]
[tex]y + 6 = -7x + 28[/tex]
Make y the subject
[tex]y = -7x + 28-6[/tex]
[tex]y = -7x + 22[/tex]
