For each equation, (a) give a table with at least three ordere...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

2x + 3y = 5

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following equation sketch its graph by using a table of ordered pairs. Our equation is nine X plus 12 Y equals 18. And we were are given a blank coordinate plane. We have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle. The units labeled for our X axis are from negative five to positive five and the units labeled for our Y axis are also from negative five to positive five. All right. So we are asked to sketch this by using a table of ordered pairs. So we'll have two columns in our table. One is the X values and one is the Y values. Now, we look at our equation and we recognize from previous lessons that that's an equation for a line. And when we're graphing a line, we only need two points. And often the easiest ones to find are the X intercept and the Y intercept, we find the Y intercept by plugging in zero for X and we find the X intercept by plugging in zero for Y. So with those two points we'll be able to graph it. Let's start by finding the Y intercept, we'll still have the nine. But now that's multiplied not by X, but by zero and then still have plus 12, Y equals 18, nine, multiplied by zero is zero. So we've got 12, Y equals 18, dividing both sides by 12. And on the left, we have Y equals and on the right 18 divided by can simplify, it, can simplify to three halves. We could write it as 1.5 their equivalent. But now we have that 1st 0.01 0.5 plotting that point from the origin will go neither left nor right for our X value of zero and will go up 1.5 for our Y value of 1.5 or three halves. All right, we found our Y intercept. Now let's find our X intercept. So back to our equation. Now we're plugging zero in for Y we'll have nine X plus 12 multiplied not by Y, but by zero equals 18, 12, multiplied by zero is nothing. So we just have nine, X equals 18. Solving for X will divide both sides by nine and we get X equals 18, divided by nine is two. So when Y equals zero, X equals two, there's our second ordered pair. Looking at our graph for our X value of two, we go from the origin to the right two units. And for our Y value of zero, we go neither up nor down. So there's our 0.20. Now, we just need to connect the dots. So we'll draw a line heading toward negative infinity for our X values, but positive infinity for our Y values. And that's going to pass through our point of 0, 1.5 and then it passes through our 0. and then it heads toward positive infinity for the X values and negative infinity for the Y values. And that's our graph of nine XX plus 12 Y equals 18. Well done. We'll catch you on the next one.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
2x + 3y = 5

Key Concepts

Linear Equations in Two Variables

Finding Ordered Pairs (Solutions)

Graphing Linear Equations

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