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

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.

y = ½ x - 2

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 Y equals 1/ X minus nine. And we're asked to use a table of ordered pairs. So we'll create a table, it'll have an X column and A Y column. And we look at our equation and we recognize that this is an equation of a line. When we are graphing a line, we only need two points. And often the easiest two points to determine are the X intercept and the Y intercept, we find the Y intercept by plugging zero in for X. And we find the X intercept by plugging zero in for Y. So let's go ahead and find the Y intercept. First. We'll plug zero in for X. So we'll have Y equals 1/9. Now multiplied by zero instead of X minus 9, 1/9 multiplied by zero is zero and zero minus nine is just negative nine. So we have Y equals negative nine. So when X equals zero, Y equals negative nine, there's one of our points. Now let's find the other one. We'll find our X intercept by plugging zero. And for Y so instead of Y equals it will be zero equals, we'll still have 1/9 X minus nine. On the right hand side, solving for X, let's first add nine to both sides of the equation. So we'll have nine equals 1/9 X. And then to get rid of that 1/9 X, we're going to multiply both sides by nine on the left nine, multiplied by nine is 81 and that equals on the right 1/ multiplied by nine is one. So it's just X. So when Y equals zero, X equals 81 and now this is why it helps sometimes to draw our graph after we figure out what our points are because that's a huge scale. So for drawing our coordinate plane will have a vertical Y axis and a horizontal X axis. And they come together at the origin. And we see for our X axis, our scale, we have to get all the way out to a positive 81. What we can do in this situation is we can move our Y axis a bit to the left giving us a little bit more room. So now our Y axis is pretty far to the left on our graph and that's fine. And we can draw our unit labels from the origin. Let's label the positive part of our X axis by every units. So we'll have a positive 10, 20 30 50 70 and 80. And now for our y axis, we can label it with the same scale. It doesn't have to be, but we can go to the negative part of the Y axis. We can have a negative 10, negative 20 negative negative 40. And then above the X axis along the Y axis will have a positive 10, 20 30 40. And then on the X axis, we could draw one unit to the left of that, which would be a negative 10. All right. Now let's plot our points. Our first point is zero, negative nine from the origin. We'll go neither left nor right for our X value of zero. And we'll go down nine units which is just before negative 10. Our other 0.81 0 from the origin will go to the right 81 units that's just past the 80. And we go neither up nor down for our Y value of zero. And we have our two points. Now, we just need to connect them. So we have our line will be heading toward negative infinity for both X and Y. And then it passes through our 0.0 negative nine and then it will pass through our point. My, it's not super straight, but you can imagine it is passes through our 0.81 0 and then continues toward positive infinity for both X and Y. And you can just imagine that that's a straight line, but there is our graph of Y equals 1/9 X minus nine. 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. y = ½ x - 2

Key Concepts

Ordered Pairs

Linear Equations

Graphing Linear Equations

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