SOLUTION: Write the equation of each line. Give the answer in standard form using only integers as the coefficients. The line through (3,4) that is parallel to the line 5x+3y=9 The ans

Question 118013: Write the equation of each line. Give the answer in standard form using only integers as the coefficients.
The line through (3,4) that is parallel to the line 5x+3y=9
The answer is 5x+3y=27
How do I work the problem to get the above answer?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First convert 5x+3y=9 into slope-intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)

Start with the given equation

Subtract 5x from both sides

Simplify

Divide both sides by 3 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

Now let's find the equation of the line through (3,4) that is parallel to the line

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (3,4), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

where m is the slope and (,) is the given point

Plug in , , and

Distribute

Multiply

Add to both sides to isolate y

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is parallel to and goes through (,) is

So here are the graphs of the equations and

graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

Now let's convert to standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)

Start with the given equation

Multiply both sides by the LCD 3

Distribute and multiply

Add 5x to both sides

Simplify

The original equation (slope-intercept form) is equivalent to (standard form where A > 0)

The equation is in the form where , and

So the answer is
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