Question 1014715: Find the equation of the line that passes through the point (2,2) and the x-intercept is twice the y-intercept.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the x-intercept is equal to 2 * the y-intercept.
the x-intercept is the value of x when y is equal to 0.
the y-intercept is the value of y when x is equal to 0.
the coordinate point of the y-intercept is (0,y)
the coordinate point of the x-intercept is (x,0)
this means that the y-intercept is equal to y and the x-intercept is equal to x.
since the x intercept is two times the y intercept, then the x-intercept can be shown as 2y, and the coordinate point of the x-intercept becomes (2y,0).
the coordinate point of the y-intercept is (0,y).
the coordinate point of the x-intercept is (2y,0).
the slope is the change in the value of y divided by the corresponding change in the value of x.
when you go from (0,y) to (2y,0), then the change in the value of y is equal to 0 - y = -y and the change in the value of x is equal to 2y - 0 = 2y.
the slope is therefore -y / 2y which is equal to -1/2.
now that we have the slope, we can figure out the rest of the equation.
the general form of the slope intercept form of the equation of a straight line is y = mx + b.
m is the slope and b is the y-intercept.
the line goes through the point (2,2).
the slope is -1/2.
when the slope is equal to -1/2, the general equation becomes y = -1/2 * x + b
when the line goes through the point (2,2), you can replace y with 2 and x with 2 to get 2 = -1/2 * 2 + b
simplify to get 2 = -1 + b
add 1 to both sides of this eqaution to get 3 = b
your y-intercept is equal to 3, therefore the slope intercept form of the equation of this particular straight line is y = -1/2 * x + 3.
the y-intercept is the value of y when x is equal to 0.
when x = 0, the equation of the line becomes y = -1/2 * 0 + 3 which results in y = 3.
the y-intercept is equal to 3.
the x-intercept is the value of x when y is equal to 0.
when y = 0, the equation becomes 0 = -1/2 * x + 3
subtract 3 from both sides of this equation to get -3 = -1/2 * x
divide both sides of this equation by -1/2 to get 6 = x
when y = 0, x = 6
the x-intercept of the equation is x = 6.
you have:
the y-intercept is 3.
the x-intercept is 6.
the x-intercept is equal to two times the y-intercept.
all requirements of the problem have been satisfied.
your solution is that the equation of the line that passes through the point (2,2) and has an x-intercept that is twice the value of the y-intercept is y = -1/2 * x + 3.
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