Transcription
We have the equation -5x + 4y = 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 = 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 = 0.
So to figure out the intercepts, let's set y = 0 in this equation and solve for x, and then let's set x = 0 and then solve for y. So when y = 0, what does this equation become? I'll do it in orange. You get -5x + 4y. Well, we're saying y is 0, so 4 * 0 = 0, so we can just not write that. So let me just rewrite it. So we have -5x = 20. We can divide both sides of this equation by -5. The -5s cancel out, that was the whole point behind dividing by -5, and we get x = 20 / -5 = -4. So when y = 0, we saw that right there, x = -4. Or if we wanted to plot that point, we always put the x coordinate first, so that would be the point (-4, 0).
So let me graph that. So if we go 1, 2, 3, 4. That's -4. And then the y value is just 0, so that point is right over there. That is the x-intercept; y = 0, x = -4. Notice we're intersecting the x-axis.
Now let's do the exact same thing for the y-intercept. Let's set x = 0, so if we set x = 0, we have -5 * 0 + 4y = 20. Well, anything times 0 is 0, so we can just put that out of the way. And remember, this was setting x = 0; we're doing the y-intercept now. So this just simplifies to 4y = 20. We can divide both sides of this equation by 4 to get rid of this 4 right there, and you get y = 20/4 = 5. So when x = 0, y = 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 = 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 as 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.