SOLUTION: Here is the question I'm stuck on: Give an equation of each line described: a) Through the point (2,5) with slope -3/4 b) through the points (3,-1) and (0,6) c) horizon

Question 978968: Here is the question I'm stuck on:
Give an equation of each line described:
a) Through the point (2,5) with slope -3/4
b) through the points (3,-1) and (0,6)
c) horizontal line through (-2,-7)
d) line through the point (6,5) and parallel to the line 2x + 3y = 7
e) line through the point (4,1) and perpendicular to the line x + 5y = 1

That is all. Thank you so much for taking time out of your day to help me!
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
a) Through the point (,) with slope

if slope , we have

now use given point (,)=(,) and find

so, your equation is

b) through the points (,) and (,)

Solved by pluggable solver: Find the equation of line going through points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (3, -1) and (x2, y2) = (0, 6).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(-2.33333333333333)x + (6)

Your graph:

c) horizontal line through (,)
For a horizontal line equation will be where is a constant.
For the line to pass through the point (,) should be equal to .
Your line should be

d) line through the point (,) and 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 (6,5), 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

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 (,)

e) line through the point (,) and perpendicular to the line

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 (4,1), 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

Combine like terms

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 (,)

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