Question

How do I solve this to create an equation in standard form?? plz help me explain this step by step. Thank you

Answer 1

4x + y = 28

Explanation:

First, you need to find the x intercept in 2x + 3y = 14.

To find the x intercept in a standard form (Ax+By=C) equation, remove the y term and solve for x:

2x + 3y = 14

2x = 14

x = 7

Now you know that the line goes through the point (7, 0)

Then you need to find the slope of the line. It is perpendicular to 2y =
`(1)/(2)`x - 5. First, isolate the y to put it in slope intercept form (y=mx+b):

2y =
`(1)/(2)`x - 5

y =
`(1)/(4)`x -
`(5)/(2)`

Original slope is
`(1)/(4)`

To find the perpendicular slope, find the opposite reciprocal of the original slope:

`(1)/(2)` ---> -
`(4)/(1)`

Slope is -4

Rewrite the equation in point slope form (y=a(x-h)+k):

y = -4(x-7)

Expand and rearrange into standard form:

y = -4(x-7)

y = -4x + 28

4x + y = 28