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

Question 252628: Find an equation of the line passing through the point (5,4) and parallel to the line whose equation
is 2x + y = 3.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

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

Distribute

Multiply

Add 4 to 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

.

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