In math class, Emma and Angelle pair as a group. Emma’s task is to graph (72)x−(92)=2y and Angelle’s task is to graph 4y=7x−9 . After they complete their graphs, they compare their work. They both get exactly the same graph. What is the solution of (72)x−(92)=2y and 4y=7x−9 ?
To compare the given equations, we need to put them in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For the equation (72)x - (92) = 2y:
We start by isolating y:
(72)x - (92) = 2y
Divide both sides by 2:
(36)x - 46 = y
So the slope-intercept form of the first equation is y = (36)x - 46.
For the equation 4y = 7x - 9:
We divide both sides by 4:
y = (7/4)x - (9/4)
So the slope-intercept form of the second equation is y = (7/4)x - (9/4).
Now we can compare the two equations:
y = (36)x - 46
y = (7/4)x - (9/4)
Since both equations have the same slope (36 and 7/4), we can conclude that the two equations represent the same line.
Therefore, the solution to the equations (72)x - (92) = 2y and 4y = 7x - 9 is any point on the line represented by the equations.