The x{\displaystyle x}-coordinate tells you how far away the point is horizontally from the y{\displaystyle y}-axis. The y{\displaystyle y}-coordinate tells you how far away the point is vertically from the x{\displaystyle x}-axis.
For example, the equation 5x+y=1{\displaystyle 5x+y=1} is a linear equation. If you see a “−{\displaystyle -}” instead of a “+{\displaystyle +}”, that means the y{\displaystyle y} coordinate is negative. If you’re working on a problem that asks you to determine whether a given ordered pair is a solution to the equation provided, you’d just plug in the numbers for x{\displaystyle x} and y{\displaystyle y} and see if they worked.
Start by subtracting 5x{\displaystyle 5x} from each side to get the y{\displaystyle y} by itself:5x+y−5x=1−5x{\displaystyle 5x+y-5x=1-5x} Simplify: y=1−5x{\displaystyle y=1-5x} Almost there! Swap the order of the expression so it matches the slope-intercept form: y=−5x+1{\displaystyle y=-5x+1} You might recognize this as slope-intercept form. It’s also referred to as function form. [5] X Research source
Don’t make this too hard on yourself! Choose a simple number, like 1{\displaystyle 1}. For example, if you’re working with y=1−5x{\displaystyle y=1-5x}, you could replace the x{\displaystyle x} with 1{\displaystyle 1} and get y=1−5(1){\displaystyle y=1-5(1)}.
For example, if you chose 1{\displaystyle 1} for the x{\displaystyle x} value in y=1−5x{\displaystyle y=1-5x}, you would have y=1−5(1)=1−5=−4{\displaystyle y=1-5(1)=1-5=-4}. So y=−4{\displaystyle y=-4}.
To continue the previous example, your ordered pair would be (1,−4){\displaystyle (1,-4)}. You might have problems that ask you to find several ordered pairs that are solutions to the linear equation. Find the other ordered pairs the same way you did with the first, choosing a new value for x{\displaystyle x} and then solving for y{\displaystyle y}.
Quadrant I: the upper-right quadrant of the plane; all points in this quadrant have positive x{\displaystyle x} coordinates and positive y{\displaystyle y} coordinates (+,+){\displaystyle (+,+)} Quadrant II: the upper-left quadrant of the plane; all points in this quadrant have negative x{\displaystyle x} coordinates and positive y{\displaystyle y} coordinates (+,−){\displaystyle (+,-)} Quadrant III: the lower-left quadrant of the plane; all points in this quadrant have negative x{\displaystyle x} coordinates and negative y{\displaystyle y} coordinates (−,−){\displaystyle (-,-)} Quadrant IV: the lower-right quadrant of the plane; all points in this quadrant have positive x{\displaystyle x} coordinates and negative y{\displaystyle y} coordinates (+,−){\displaystyle (+,-)}
The sign in front of the x{\displaystyle x} coordinate tells you which direction to go. If the x{\displaystyle x} coordinate is positive, you’ll go right from the y{\displaystyle y} axis. For negative numbers, you’ll go left. You can also think of right as east and left as west. This is helpful with word problems that involve directions.
If the y{\displaystyle y} coordinate is positive, you’ll go up from the x{\displaystyle x} axis. A negative y{\displaystyle y} coordinate, on the other hand, will be down or below the x{\displaystyle x} axis. In word problems that use cardinal directions, positive numbers are north and negative numbers are south.
If you have other ordered pairs, continue plotting those points as well. For example, you might have a problem where you’re supposed to plot 3 points and then draw a line connecting them.
Hint: Convert the equation from standard form to slope-intercept or function form (y=mx+b{\displaystyle y=mx+b}), then solve for y{\displaystyle y}.
Hint: In this problem, assume that “school” is the origin of the coordinate plane and each block is one line.
Hint: Let x{\displaystyle x} represent the number of tickets so you can solve for y{\displaystyle y}, the total cost.
Hint: Remember that you can choose whatever value you want for x{\displaystyle x}.
For x{\displaystyle x} of 0{\displaystyle 0} : y=4(0)−2=0−2=−2{\displaystyle y=4(0)-2=0-2=-2}, so your ordered pair is (0,−2){\displaystyle (0,-2)}. For x{\displaystyle x} of −1{\displaystyle -1} : y=4(−1)−2=−4−2=−6{\displaystyle y=4(-1)-2=-4-2=-6}, so your ordered pair is (−1,−6){\displaystyle (-1,-6)}. For x{\displaystyle x} of 2{\displaystyle 2} : y=4(2)−2=8−2=6{\displaystyle y=4(2)-2=8-2=6}, so your ordered pair is (2,6){\displaystyle (2,6)}.
Braden lives north and east of school. North is up (vertical) and east is to the right (horizontal)—that means you’re in quadrant I, where both numbers are positive. Now, all you’ve gotta do is plug in the numbers you were given to get (1,2){\displaystyle (1,2)} as your ordered pair. Riley lives south and west of school. South is down (vertical) and west is to the left (horizontal)—that means you’re in quadrant III, where both numbers are negative. Plug in the numbers provided in the problem, and you find your ordered pair is −2,−3{\displaystyle -2,-3}.
Since you were told to compute the total cost for 18{\displaystyle 18} students, you’ll plug in 18{\displaystyle 18} for x{\displaystyle x}: y=5(18)+2{\displaystyle y=5(18)+2}. Now, solve the equation: y=90+2=92{\displaystyle y=90+2=92}. The total cost for 18{\displaystyle 18} students is $92{\displaystyle $92}. Then, since 18{\displaystyle 18} was your x{\displaystyle x} value, it will be the first number of your ordered pair. As the y{\displaystyle y} value, 92{\displaystyle 92} will be the second number.
Assume you chose 1{\displaystyle 1} as one of your values of x{\displaystyle x}. Your work would look like this: y=−3(1)+24=−3+24=21{\displaystyle y=-3(1)+24=-3+24=21}. Ordered pair: (1,21){\displaystyle (1,21)} What if you chose −2{\displaystyle -2}? You’d get y=−3(−2)+24=6+24=30{\displaystyle y=-3(-2)+24=6+24=30}. Ordered pair: (−2,30){\displaystyle (-2,30)}.
