SOLUTION: 1. Consider the line passing through points ( -3,-2) and (2,5): a. Find the slope of this line b. Find the equation of this line in slope-intercept form. c. Find the x-int

Question 763076: 1. Consider the line passing through points ( -3,-2) and (2,5):
a. Find the slope of this line
b. Find the equation of this line in slope-intercept form.
c. Find the x-intercept and y-intercept of this line.
d. Graph the linear equation
e. Find an equation of the line in point-slope from passing through (6,4) and perpendicular to this line.
Thanks.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
a.

Solved by pluggable solver: Finding the slope

Slope of the line through the points (-3, -2) and (2, 5)

Answer: Slope is

so, the slope is
b.

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, -2) and (x2, y2) = (2, 5).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .

y=(1.4)x + (2.2)

Your graph:

c. x-intercept and y-intercept
....plug in to find

so, is at (,)
....plug in to find

is at (,)
d. Graph the linear equation

e. Find an equation of the line in point-slope from passing through (,) and perpendicular to this 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 (6,4), 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 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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