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

Answer:

4x + y = 28

Step-by-step 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 = $\frac{1}{2}$x - 5. First, isolate the y to put it in slope intercept form (y=mx+b):

2y = $\frac{1}{2}$x - 5

y = $\frac{1}{4}$x - $\frac{5}{2}$

Original slope is $\frac{1}{4}$

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

$\frac{1}{2}$ ---> -$\frac{4}{1}$

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