Question 430081
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:


{{{graph(600,600,-10,10,-10,10,(-5/4)x + (22/4))}}}


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.