SOLUTION: How do I write the slope intercpt form of an equation of the line that passes throught the given point and is parallel to the graph of the equation (4,-6),y=-3/4x+1

Question 253688: How do I write the slope intercpt form of an equation of the line that passes throught the given point and is parallel to the graph of the equation
(4,-6),y=-3/4x+1
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

Distribute

Multiply

Subtract 6 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

.

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