Question 1008979
y=(4/7)x -(2/7) (red line on graph below)
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If the above equation is correct:
Slope intercept form:
y=mx+b
Where m = the slope = 4/7, y-intercept at (-2/7)
Parallel lines have the same slope,
so the solution will have the form:
y=(4/7)x+b
We know (3,-5) is a solution for the equation,
so we use this point to solve for b:
-5=(4/7)3+b
-5=(12/7)+b
(-35/7)-(12/7)=b
-47/7=b
Put this b in the equation:
y=(4/7)x+b
y=(4/7)x-(47/7) (green line on graph below)
slope=(4/7), y-intercept at (-47/7)
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ANSWER: The equation of the parallel line through (3,-5) is:
y=(4/7)x-(47/7)
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{{{ graph( 500, 500, -10, 10, -10, 10, (4/7)x -(2/7),(4/7)x-(47/7) ) }}}