x-intercepts and y-intercepts
We have the equation negative 5x plus 4y is equal to 20, and we're told to find the intercepts of this equation. So we have to find the intercepts and then use the intercepts to graph this line on the coordinate plane. So then graph the line. So whenever someone talks about intercepts, they're talking about where you're intersecting the x and the y-axes. So let me label my axes here, so this is the x-axis and that is the y-axis there. And when I intersect the x-axis, what's going on? What is my y value when I'm at the x-axis? Well, my y value is 0, I'm not above or below the x-axis. Let me write this down. The x-intercept is when y is equal to 0, right? And then by that same argument, what's the y-intercept? Well, if I'm somewhere along the y-axis, what's my x value? Well, I'm not to the right or the left, so my x value has to be 0, so the y-intercept occurs when x is equal to 0. So to figure out the intercepts, let's set y equal to 0 in this equation and solve for x, and then let's set x is equal to 0 and then solve for y. So when y is equal to 0, what does this equation become? I'll do it in orange. You get negative 5x plus 4y. Well we're saying y is 0, so 4 times 0 is equal to 20. 4 times 0 is just 0, so we can just not write that. So let me just rewrite it. So we have negative 5x is equal to 20. We can divide both sides of this equation by negative 5. The negative 5 cancel out, that was the whole point behind dividing by negative 5, and we get x is equal to 20 divided by negative 5 is negative 4. So when y is equal to 0, we saw that right there, x is equal to negative 4. Or if we wanted to plot that point, we always put the x coordinate first, so that would be the point negative 4 comma 0. So let me graph that. So if we go 1, 2, 3, 4. That's a negative 4. And then the y value is just 0, so that point is right over there. That is the x-intercept, y is 0, x is negative 4. Notice we're intersecting the x-axis. Now let's do the exact same thing for the y-intercept. Let's set x equal to 0, so if we set x is equal to 0, we have negative 5 times 0 plus 4y is equal to 20. Well, anything times 0 is 0, so we can just put that out of the way. And remember, this was setting x is equal to 0, we're doing the y-intercept now. So this just simplifies to 4y is equal to 20. We can divide both sides of this equation by 4 to get rid of this 4 right there, and you get y is equal to 20 over 4, which is 5. So when x is equal to 0, y is equal to 5. So the point 0, 5 is on the graph for this line. So 0, 5. x is 0 and y is 1, 2, 3, 4, 5, right over there. And notice, when x is 0, we're right on the y-axis, this is our y-intercept right over there. And if we graph the line, all you need is two points to graph any line, so we just have to connect the dots and that is our line. So let me connect the dots, trying my best to draw as straight of a line is I can-- well, I can do a better job than that-- to draw as straight of a line as I can. And that's the graph of this equation using the x-intercept and the y-intercept.