Graph each inequality. 4y - 3x ≤ 5

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Hello, today we're gonna be drawing the graph for the given inequality. So what we are given is six Y minus five X is less than or equal to 11. Now, currently, our inequality matches the form of an equation of a line in standard form. If we were to rewrite this using an equal sign, we get the equation six Y minus five X is equal to 11. Now, in this case here, if we wanted to get the equation of a line, we will want to solve for our Y variable. And the purpose of showing this is to show that we can use the same methods for the inequalities. Since the inequality matches the form of this equation of a line in standard form. If we solve for the Y variable here, then we can represent the inequality in a form that is similar to the equation of a line. So let's go ahead and solve for why in our given inequality, the first step is to add five X to both sides of the inequality that is going to give us six Y is less than or equal to five X plus 11. Then what we wanna do is we wanna isolate Y and we can do that by dividing every term by positive six, that is going to give us Y less than, or equal to 5/6 X plus 11/6. Now, if we were to replace the inequality sign with an equal sign, this inequality matches the form of an equation of a line and the equation of a line is going to have the form Y is equal to 5/6, X plus 11/6. So here is the Y intercept and 5/6 is going to be the slope of the line. So we can represent the graph of the inequality as an equation of the line. So let's go ahead and start by drawing the axis. And the first thing we're gonna want to do is to plot the Y intercept. Now the Y intercept is given to us as 11/6. And if we were to estimate this value 11/6 is roughly equal to 1.8. So we can say that the Y intercept is going to be here at zero comma 1.8. Then we wanna go ahead and increase the slope. See we're going to have a positive slope slope because we have a positive coefficient in front of X. This slope is gonna go up five units and go to the right six units. So the next point in the line is gonna be estimate at six comma 6.8. And so we can go ahead and connect the dots. But when we're dealing with inequalities, we need to ask ourselves, do we want to include the points that are along the line of the graph? Well, in this case here, the inequality uses the less than or equal to sign. And what that means is that the solutions to this inequality graph can be on the line itself or above slash below the line. So since we can include the values that are along the line, we're going to connect these dots using a solid line. So that's going to be the rough shape of our inequality. But now we need to ask ourselves, do we also want to include all the values below the graph or all the values above the graph? Well, the easiest way to determine that is to pick a testing point above or below the graph, plug it into our inequality and see if it satisfies the inequality. The easiest testing point to pick here is going to be the origin zero comma zero. So if we plug in zero comma zero into our inequality, we get zero is less than or equal to 5/ times zero plus 11/6. Now, anything times zero is just going to be zero. So 5/6 times zero is gonna cancel itself out leaving us with zero, less than or equal to 11/6. Now, since this is a true inequality. That means our testing point satisfies the inequality. And that means that we're going to want to include the region that is below the graph. And so if we shade this in this is going to be the complete graph for our inequality. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Graph each inequality. 4y - 3x ≤ 5

Key Concepts

Inequalities

Graphing Linear Inequalities

Slope-Intercept Form

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