Answer:
[tex]y = 2x + 4[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (2,8)[/tex]
[tex](x_2,y_2) = (4,12)[/tex]
Required
Determine the line equation
This will be solved using linear interpolation as follows:
[tex]\frac{y - y_1}{x - x_1} =\frac{y_2 - y_1}{x _2- x_1}[/tex]
Where:
[tex](x_1,y_1) = (2,8)[/tex]
[tex](x_2,y_2) = (4,12)[/tex]
So, we have:
[tex]\frac{y - 8}{x - 2} =\frac{12 - 8}{4-2}[/tex]
[tex]\frac{y - 8}{x - 2} =\frac{4}{2}[/tex]
[tex]\frac{y - 8}{x - 2} =2[/tex]
Cross Multiply:
[tex]y - 8 = 2(x - 2)[/tex]
Open bracket
[tex]y - 8 = 2x - 4[/tex]
Make y the subject
[tex]y = 2x - 4+8[/tex]
[tex]y = 2x + 4[/tex]
