Match each inequality with the appropriate calculator graph in...

Question

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Accepted Answer

Hello everybody. Everything. All right today that we're going to be talking about this question that states draw the graph for the given inequality where the inequality is Y is less than or equal to negative two X minus four. Now, the first thing I'll do is just replace that lesson or equal to sign with an equal sign just for the sake of the question. So I have that Y equals negative two X minus four. Now something we should know is that because we have less than or equal to in our original equation, this means this is a non strict inequality. If it was less than without the equal sign or greater than without the equal sign. That's what we call a strict inequality. But because it's less than or equal to, it is non strict. That's just something we should note for later in the graph. Now we have Y equals negative two X minus four which resembles the equation for a line where we know that an equation for our line. Oh Right on the side here, I'll recall that a line equation is Y equals M X plus B where um is equal to the slope and the being is equal to the Y intercept. And I put Y Y I N T as an abbreviation. So we know that we have the equation for a line. So we know our graph will look like a line. So I'm just going to plug in a couple of different points to just see what a line would look like. I'll first off for the X intercept to see what that would be. So for that, we'll just plug in zero for our Y. So we'll have zero is equal to negative two, X minus four and we'll move the minus four over to the left hand side to have four is equal to negative two, X. And then if we divide both sides by negative two, we'll have that X is equal to negative two or the point negative two comma zero. And that'll be our first point or our Y in our X intercept. And now we'll look at our Y intercept for that. We do the same thing except we instead of plugging in zero for the Y, we plug in zero for the X. So I have that Y is equal to negative two, multiplied by zero minus four, which is Y equals negative four because anything multiplied by zero is zero or the point zero comma negative four. And that will be R Y intercept. Now, with this information, we already have two points and we know that we have a line. So we can go ahead and start graphing. So we draw a Y axis and an X axis and we'll plug in a point at a Y of negative four zero comma negative four. And we'll plug in another point at an X of negative two, negative two comma zero. And like I said, since we know we have a line, we can connect those two points. And as we mentioned earlier in the question, because this is a non strict inequality, we can use a solid solid line. So that's the point of keeping track of what type of inequality we have. So we use a solid line to connect both points and we extend past both of them. And now we, since this is inequality, we know that we have to shade a region. So we'll test a point in this case, we'll test the 0.0 comma zero just to see if that point would work in the inequality. And what I mean by that is we just plug in zero for the Y. So we'll have an N D X because our point, our test point is zero comma zero. So we'll have zero is less than or equal to. So we'll go back to the inequality. Now, zero is less than or equal to negative two, multiplied by zero minus four. And we'll have that zero is less than or equal to negative four, which is not true. So the 0.0 comma zero would not work. Therefore, we have to shade the region under our line. So under and to the left hand side of our line is where we will shade the region since we tested zero, comma zero, which is above our line. And that didn't work. That means above the line will not work. So we shade that region and will be left with a graph for art inequality. So I hope that was helpful. And until next time.

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Key Concepts

Graphing Linear Inequalities

Slope-Intercept Form

Testing Points to Determine Shading

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