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 = [tex]\frac{1}{2}[/tex]x - 5. First, isolate the y to put it in slope intercept form (y=mx+b):
2y = [tex]\frac{1}{2}[/tex]x - 5
y = [tex]\frac{1}{4}[/tex]x - [tex]\frac{5}{2}[/tex]
Original slope is [tex]\frac{1}{4}[/tex]
To find the perpendicular slope, find the opposite reciprocal of the original slope:
[tex]\frac{1}{2}[/tex] ---> -[tex]\frac{4}{1}[/tex]
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
