SOLUTION: Find the equation of the lines if: The line is parallel to the line 3x-7y=15 and has an x-intercept of -5.

Question 87577: Find the equation of the lines if:
The line is parallel to the line 3x-7y=15 and has an x-intercept of -5.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First convert 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 3x from both sides

Simplify

Divide both sides by -7 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.

Since the line has an x-intercept of -5, this means the line goes through the point (-5,0)

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 (-5,0), 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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