Question 458213
Write an equation in standard form for the line described. through (7,9), perpendicular to 4x+y=7
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Standard form for a straight line: y=mx+b, m= slope, and b= y-intercept
For given line:
4x+y=7
y=-4x+7
slope=-4
slope of line perpendicular to this line is the negative reciprocal=-(-1/4)=1/4
for line thru (7,9)
y=x/4+b
plug in x & y from given point (7,9)
9=7/4+b
b=9-7/4=36/4-7/4=32/4=8
Equation:
y=x/4+8
See graph of the two lines below as a visual check on the answer:

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{{{ graph( 300, 300, -10, 10, -10, 10,-4x+7,x/4+8) }}}