SOLUTION: I really need some help with this problem: write the slope/intercept form of the equations of the lines described. 1. through: (-2,1) parallel to y=1/2x + 5 2. through:

Question 1003269: I really need some help with this problem:

write the slope/intercept form of the equations of the lines described.
1. through: (-2,1) parallel to y=1/2x + 5
2. through: (3, -5) perpendicular to y= 4/3x + 3
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1. through: (,) parallel to

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 (-2,1), 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 (,)

2. through: (, ) perpendicular to

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

Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula:

where is the perpendicular slope

So plug in the given slope to find the perpendicular slope

When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second

Multiply the fractions.

So the perpendicular slope is

So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (3,-5), 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

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is perpendicular 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 perpendicular to the given graph and goes through (,)

RELATED QUESTIONS
How do I write the equations of the line, in slope-intercept form, A) which goes... (answered by checkley77)

hi, i really need help with this equation. write an equation in slope-intercept form... (answered by stanbon,sarahschober)

I want to know step by step on how to do this problem. The directions are find the slope- (answered by josgarithmetic)

I REALLY need help with parallel & Perpendicular lines! Here's what it says: Write an... (answered by ankor@dixie-net.com)

Write the slope intercept form of {{{3x=16+4y}}} I need help with this... (answered by Nate)

5. Use the point-slope from to write an equation of the line the given properties. slope (answered by stanbon,Shana-D77)

hi! i need help with this problem. "determine the equation of the line described. Put (answered by Mathtut)

write the equation of the line with the slope-2 and y-intercept of (0,0) then graph the... (answered by jim_thompson5910)

Write the slope intercept form of the equation of the described line. Through (3,4)... (answered by josgarithmetic)