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Question 1111887: Please help me to do this :
Thank you.
Question 1:
a) Explain how you would find an equation of a line passing through the point (-1,2) and perpendicular to the line 2x-5y=9.
b) Complete the process to find the equation of the perpendicular line. Show all work and put the final answer in slope intercept form.
Question 2:
Given the function: g(x)=2x^2-2x+6
Find and show all work in computing:
g(0)=____ This represents the ordered pair ( , )
g(-2)=____ This represents the ordered pair ( , )
g(6)=____ This represents the ordered pair ( , )
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Question 1:
a) Explain how you would find an equation of a line passing through the point (-1,2) and perpendicular to the line 2x-5y=9.
Step 1, find the slope of the line.
The slope of the perpendicular line is the negative inverse, call it m.
Use y-y1 = m*(x-x1) where (x1,y1) is the point.
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b) Complete the process to find the equation of the perpendicular line. Show all work and put the final answer in slope intercept form.
--- Do that.
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Question 2:
Given the function: g(x)=2x^2-2x+6
Find and show all work in computing:
g(0)=____ This represents the ordered pair ( , )
Wherever you see x, sub 0.
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g(-2)=____ This represents the ordered pair ( , )
Wherever you see x, sub -2.
---
g(6)=____ This represents the ordered pair ( , )
Wherever you see x, sub 6.
---
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! Question 1:
a) Explain how you would find an equation of a line passing through the point (-1,2) and perpendicular to the line 2x-5y=9.
b) Complete the process to find the equation of the perpendicular line. Show all work and put the final answer in slope intercept form.
the point that the line passes through is (-1,2).
the line it has to be perpenedicular to is 2x - 5y = 9
convert 2x - 5y = 9 to slope intercept form.
slope intercept form is y = mx + b
m is the slope
b is the y-intercept
start with 2x - 5y = 9
subtract 9 from both sides and add 5 to both sides of this equation to get:
2x - 9 = 5y
divide both sides of the equation by 5 to get:
2/5 * x - 9/5 = y
commute the equation to get:
y = 2/5 * x - 9/5
the equation is now in slope intercept form.
the slope is 2/5.
the line perpendicular to it will have a slope that is a negative reciprocal of 2/5.
that would make the slope of the line perpendicular to it equal to -5/2.
the slope intercept form of the equation of that line will be:
y = -5/2 * x + b
the line perpendicular to the graph of the original equation will pass through the point (-1,2).
that coordinate point is in (x,y) format.
the x-coordinate of the point is -1.
the y-coordinate of the point is 2.
in the equation of y = -5/2 * x + b, replace y with 2 and replace x with -1 to get:
the equation of y = -5/2 * x + b becomes:
2 = -5/2 * -1 + b, after you replace y with 2 and x with -1.
simplify to get:
2 = 5/2 + b
subtract 5/2 from both sides of this equation to get:
2 - 5/2 = b
simplify to get:
4/2 - 5/2 = b
simplify further to get:
-1/2 = b
equation of the line perpendicular to y = 2/5 * x - 9/5 should be:
y = -5/2 * x -1/2
the graph of the original equation in slope intercept form and the graph of the equation perpendicular to the original equation is shown below.
the red line is the graph of the original equation.
the blued line is the graph of the equation perpendicular to it.
you can see that the line perpendicular to the graph of the original equation passed through the point (-1,2).
you can see that the graph of the original equation has a y-intercept of -1.8.
-1.8 is the same as -9/5, which is the y-intercept of the original equation.
you can see that the graph of the equation perpendicular to the original equation has a y-intercept of -.5.
-.5 is the same as - 1/2, which is the y-intercept of the equation perpendicular to the original equation.
the graph shows that calculations were correct.
Question 2:
Given the function: g(x)=2x^2-2x+6
Find and show all work in computing:
to find the ordered pairs, you replace x with the values that you are evaluating in the equation of g(x) = 2x^2 - 2x + 6
for g(0), replace x with 0 in the equation of g(x) = 2x^2 - 2x + 6 to get:
g(0) = 2*0^2 - 2*0 + 6.
this results in g(0) = 6
the ordered pair would be (0,6)
for g(-2), replace x with -2 in the equation of g(x) = 2x^2 - 2x + 6 to get:
g(-2) = 2*(-2)^2 - 2*(-2) + 6.
this results in g(-2) = 18
the ordered pair would be (-2,18)
for g(6), replace x with 6 in the equation of g(x) = 2x^2 - 2x + 6 to get:
g(6) = 2*6^2 - 2*6 + 6.
this results in g(6) = 66
the ordered pair would be (6,66)
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