SOLUTION: Find an equation of the line that is parallel to the line y=4x+5 and that passes through the point (-3,-2).

Question 336496: Find an equation of the line that is parallel to the line y=4x+5 and that passes through the point (-3,-2).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

Rewrite as

Distribute

Multiply

Subtract 2 from both sides.

Combine like terms.

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

.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim
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