SOLUTION: Find the equation of the line in point slope form that passes through (4,3)and is parallel to the line 3x-y=7.

Question 153218: Find the equation of the line in point slope form that passes through (4,3)and is parallel to the line 3x-y=7.
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.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

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 3 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

.

RELATED QUESTIONS
Find the equation of the line, in slope-intercept form, that passes through the point (3, (answered by tanimachatterjee)

find the equation in slope-intercept form of the line that passes through the point (-1, (answered by solver91311,ewatrrr,josmiceli)

Find the midpoint of the line segment with endpoints (-8,4) and (-2,-6) Find the... (answered by josgarithmetic)

What is the equation of a line that is parallel to the line y=3x+9 and NEVER passes... (answered by Alan3354)

Write an equation in slope-intercept form for the line that is parallel to the given line (answered by Fombitz)

Write the equation of a line in slope-intercept form that is parallel to the line y=3x+2... (answered by jim_thompson5910)

write in slope-intercept form the equation of the line that passes through the given... (answered by mananth)

Find an equation of the line in point slope form that passes through (4,3) and is... (answered by Alan3354)

I don't understand this. write an equation in slope-intercept form of the line that... (answered by nyc_function)