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Question 430081: Which point lies on the line represented by the equation below?
5x + 4y = 22
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a whole bunch of points lie on the line represented by the equation.
to find them, you need to solve for either y or x.
most time you solve for y.
this makes y the dependent variable and x the independent variable.
being independent, you can choose any value you want for x and then use the equation to solve for y.
you could eave the equation as is and then solve for y, or you can solve for y and then plug in the values for x.
we'll solve for y first and then plug values in for x to find values of y that satisfy the equation.
if the values of y satisfy the equation, then the coordinate (x,y) pair created by combining that x with that y will be on the line.
your equation is:
5x + 4y = 22
we solve for y as follows:
subtract 5x from both sides of the equation to get:
4y = -5x + 22
divide both sides of the equation by 4 to get:
y = (-5/4)x + (22/4)
you have just solved for y.
now you can take any value of x and plug it into the equation to solve for y.
we'll take x = 0.
when x = 0, the equation becomes:
y = (-5/4)*0 + (22/4) which becomes y = (22/4).
the coordinate pair of (x,y) we now have is (0,(22/4).
that point is on the line because the value of y we calculated satisfies the equation when x = 0.
that value of y, by the way, is the y-intercept of the equation. the y-intercept of the equation is the value of y when x = 0.
if we want to find the x-intercept of the equation, then we set the value of y equal to 0 and solve for x.
our equation is:
y = (-5/4)x + (22/4)
when we set y equal to 0, the equation becomes:
0 = (-5/4)x + (22/4)
subtract (22/4) from both sides of the equation to get:
-(22/4) = (-5/4)x
multiply both sides of the equation by (-4/5) to get:
-(4/5) * -(22/4) = x
multiplying these factors together, we get:
(-4 * -22) / (5*4) = x
we simplify this to get (88/20) = x
we simplify this further by dividing numerator and denominator of the fraction by 4 to get:
(22/5) = x
we commute this equation to get:
x = (22/5)
our coordinate pair for when y = 0 is going to be (x,y) = ((22/5),0).
we now have 2 points on the line.
we can find lots more points on the line by just setting x equal to some value and then solving for y.
the graph of this equation looks like this:
since (22/4) is equal to 5.5, then the coordinate pair of (0,(22/4)) is the same as (0,5.5) which is the intersection of the equation of the line with the y-axis which is also the value of y when x = 0. the graph confirms this.
since (22/5) is equal to 4.4, then the coordinate pair of ((22/5),0) is the same as (4.4,0) which is the intersection of the equation of the line with the x-axis which is also the value of x when y = 0. the graph confirms this.
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