Which line is parallel to the line whose equation is 4x+3y=7 and also passes through the point (-5,2)?

If a line is parallel to another they will have the same gradient. We can rearrange this equation into the form y=mx+c to start.

3y=-4x+7
y=-4/3x+7/3

Now we know that the gradient of the line is -4/3 so
y=-4/3x+c

Now we can substitute the points (-5,2) into this to find the y intercept

2=(-4/3 times -5)+c
2=20/3+c
-14/3=c

therefore the line is y=-4/3x-14/3

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