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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (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)



m+=+%28y%5B2%5D+-+%28y%5B1%5D%29%29%2F%28x%5B2%5D+-+%28x%5B1%5D%29%29


m+=+%285+-+%28-2%29%29%2F%282+-+%28-3%29%29


m+=+%285+%2B+2%29%2F%282+%2B+3%29


m+=+%287%29%2F%285%29


Answer: Slope is m+=+7%2F5



so, the slope is m=7%2F5=1.4
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 a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%285--2%29%2F%282--3%29+=+1.4.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 1.4%2A-3+%2Bb+=+2.2. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-2-1.4%2A-3+=+2.2.

y=(1.4)x + (2.2)

Your graph:




c. x-intercept and y-intercept
y=1.4x+%2B+2.2....plug in y=0 to find x-intercept
0=1.4x+%2B+2.2
-2.2=1.4x+
-2.2%2F1.4=x+
-1.57=x+
so, x-intercept is at (-1.57,0)
y=1.4x+%2B+2.2....plug in x=0 to find y-intercept
y=1.4%2A0+%2B+2.2
y=2.2
y-intercept is at (0,2.2)
d. Graph the linear equation
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C1.4x+%2B+2.2%29+
e. Find an equation of the line in point-slope from passing through (6,4) 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 1.4, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%281.4%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F1.4%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-0.714285714285714%2F1 Multiply the fractions.


So the perpendicular slope is -0.714285714285714



So now we know the slope of the unknown line is -0.714285714285714 (its the negative reciprocal of 1.4 from the line y=1.4%2Ax%2B2.2). 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:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-4=-0.714285714285714%2A%28x-6%29 Plug in m=-0.714285714285714, x%5B1%5D=6, and y%5B1%5D=4



y-4=-0.714285714285714%2Ax%2B%280.714285714285714%29%286%29 Distribute -0.714285714285714



y-4=-0.714285714285714%2Ax%2B4.28571428571429 Multiply



y=-0.714285714285714%2Ax%2B4.28571428571429%2B4Add 4 to both sides to isolate y

y=-0.714285714285714%2Ax%2B8.28571428571428 Combine like terms

So the equation of the line that is perpendicular to y=1.4%2Ax%2B2.2 and goes through (6,4) is y=-0.714285714285714%2Ax%2B8.28571428571428


So here are the graphs of the equations y=1.4%2Ax%2B2.2 and y=-0.714285714285714%2Ax%2B8.28571428571428




graph of the given equation y=1.4%2Ax%2B2.2 (red) and graph of the line y=-0.714285714285714%2Ax%2B8.28571428571428(green) that is perpendicular to the given graph and goes through (6,4)