SOLUTION: Which point lies on the line represented by the equation below? 5x + 4y = 22

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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