SOLUTION: (-6,5);8x=5y+2 Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b

Question 154327: (-6,5);8x=5y+2
Write an equation of the line containing the given point and the parrallel to the given line. Expess in the form y=mx+b
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 2 from both sides.

Divide both sides by 5.

Break up the fraction

Simplify

So after converting into slope-intercept form, we get

We can see that the equation has a slope and a y-intercept .

Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Add 5 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation of the line parallel to that goes through the point

is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point

.

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