SOLUTION: Write an equation in the slope intercept form if possible: The line goes through the (1,4) and is parallel to 5 + 4y = 3x

Question 102642: Write an equation in the slope intercept form if possible: The line goes through the (1,4) and is parallel to 5 + 4y = 3x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First solve for y:

Start with the given equation

Subtract 5 from both sides

Multiply both sides by to isolate y

Distribute

Multiply. So now the equation is in slope-intercept form where the slope is and the y-intercept is

Now let's find the equation of the line that is parallel to and goes through (1,4)

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 (1,4), 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 (,)

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