SOLUTION: Please HELP me solve this quesion !!! A line passes through the points (2,9) and (9,2) ~ a. Write the equation of the line. b. Write the equation of the parallel line goin

Question 730051: Please HELP me solve this quesion !!!
A line passes through the points (2,9) and (9,2) ~
a. Write the equation of the line.
b. Write the equation of the parallel line going through the origin.
c. Write the equation of the perpendicular line through (2,9).
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

a.
the equation of the line passes through the points (,) and (,)

Solved by pluggable solver: FIND EQUATION of straight line given 2 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) = (2, 9) and (x2, y2) = (9, 2).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(-1)x + (11)

Your graph:

b.

the equation of the parallel to line going through the origin (,)

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 (0,0), 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

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 (,)

c.
the equation of the perpendicular to line through (,)

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 (2,9), 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 (,)

...given line
...parallel line
...perpendicular

let's graph them all together:

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