SOLUTION: A line passes through the point (4,3) and intersects the x-axis at x=10. Where does the line intersect the y-axis? choose the answer and explain the reason to choose your respon

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: A line passes through the point (4,3) and intersects the x-axis at x=10. Where does the line intersect the y-axis? choose the answer and explain the reason to choose your respon      Log On


   

Question 486598: A line passes through the point (4,3) and intersects the x-axis at x=10. Where does the line intersect the y-axis?
choose the answer and explain the reason to choose your response
y=4.5
y=7.7
y=6
y=5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If a line passes through the point (4,3) and intersects the x-axis at x=10 or at the point (10,0), we can find the equation using these two points:

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (4,3) and (10,0)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (4,3) and (x%5B2%5D,y%5B2%5D) is the second point (10,0))


m=%280-3%29%2F%2810-4%29 Plug in y%5B2%5D=0,y%5B1%5D=3,x%5B2%5D=10,x%5B1%5D=4 (these are the coordinates of given points)


m=+-3%2F6 Subtract the terms in the numerator 0-3 to get -3. Subtract the terms in the denominator 10-4 to get 6




m=-1%2F2 Reduce



So the slope is

m=-1%2F2





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Now let's use the point-slope formula to find the equation of the line:




------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 one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-3=%28-1%2F2%29%28x-4%29 Plug in m=-1%2F2, x%5B1%5D=4, and y%5B1%5D=3 (these values are given)



y-3=%28-1%2F2%29x%2B%28-1%2F2%29%28-4%29 Distribute -1%2F2


y-3=%28-1%2F2%29x%2B2 Multiply -1%2F2 and -4 to get 4%2F2. Now reduce 4%2F2 to get 2

y=%28-1%2F2%29x%2B2%2B3 Add 3 to both sides to isolate y


y=%28-1%2F2%29x%2B5 Combine like terms 2 and 3 to get 5

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Answer:



So the equation of the line which goes through the points (4,3) and (10,0) is:y=%28-1%2F2%29x%2B5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=5


Notice if we graph the equation y=%28-1%2F2%29x%2B5 and plot the points (4,3) and (10,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B5 through the points (4,3) and (10,0)


Notice how the two points lie on the line. This graphically verifies our answer.




so, the equation in slope-intercept form is:
y=-%281%2F2%29x%2B5...the line intersect the y-axis at y=5