SOLUTION: 1. Find the equation of a line that is parallel to y= 2x-3 had has a y-intercept of 4 2. Find the equation of a line that is perpendicular y=-3x + 7 and has a y-intercept of -

Question 696671: 1. Find the equation of a line that is parallel to y= 2x-3 had has a y-intercept of 4

2. Find the equation of a line that is perpendicular y=-3x + 7 and has a y-intercept of -2

3. Find the equation of a line that is parallel to y =2x -1 and goes through the point(6,2)

4.Find the equation of a line that is perpendicular to y=1/3x + 2 and goes through the point (1,7)
Please work out all problems completely along with the solution.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

1. Find the equation of a line that is parallel to had has a y-intercept of (means it passes through point (,))

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 (0,4), 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

Combine like terms

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 (,)

2. Find the equation of a line that is perpendicular and has a y-intercept of (means it passes through point (,))

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 (0,-2), 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

Subtract from both sides to isolate y

Combine like terms

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 (,)

3. Find the equation of a line that is parallel to and goes through the point (,))

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 (6,2), 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

Combine like terms

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 (,)

4.Find the equation of a line that is perpendicular to and goes through the point (,))

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 (1,7), 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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