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We have the equation negative 5x plus 4y is equal to 20, and

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we're told to find the intercepts of this equation.

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So we have to find the intercepts and then use the

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intercepts to graph this line on the coordinate plane.

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So then graph the line.

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So whenever someone talks about intercepts, they're

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talking about where you're intersecting

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the x and the y-axes.

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So let me label my axes here, so this is the x-axis and that

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is the y-axis there.

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And when I intersect the x-axis, what's going on?

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What is my y value when I'm at the x-axis?

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Well, my y value is 0, I'm not above or below the x-axis.

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Let me write this down.

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The x-intercept is when y is equal to 0, right?

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And then by that same argument, what's the

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y-intercept?

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Well, if I'm somewhere along the y-axis, what's my x value?

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Well, I'm not to the right or the left, so my x value has to

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be 0, so the y-intercept occurs when x is equal to 0.

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So to figure out the intercepts, let's set y equal

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to 0 in this equation and solve for x, and then let's

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set x is equal to 0 and then solve for y.

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So when y is equal to 0, what does this equation become?

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I'll do it in orange.

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You get negative 5x plus 4y.

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Well we're saying y is 0, so 4 times 0 is equal to 20.

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4 times 0 is just 0, so we can just not write that.

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So let me just rewrite it.

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So we have negative 5x is equal to 20.

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We can divide both sides of this equation by negative 5.

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The negative 5 cancel out, that was the whole point

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behind dividing by negative 5, and we get x is equal to 20

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divided by negative 5 is negative 5.

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So when y is equal to 0, we saw that right there, x is

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equal to negative 5.

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Or if we wanted to plot that point, we always put the x

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coordinate first, so that would be the point

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negative 4 comma 0.

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So let me graph that.

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So if we go 1, 2, 3, 4.

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That's a negative 4.

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And then the y value is just 0, so that point

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is right over there.

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That is the x-intercept, y is 0, x is negative 4.

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Notice we're intersecting the x-axis.

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Now let's do the exact same thing for the y-intercept.

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Let's set x equal to 0, so if we set x is equal to 0, we

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have negative 5 times 0 plus 4y is equal to 20.

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Well, anything times 0 is 0, so we can just put

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that out of the way.

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And remember, this was setting x is equal to 0, we're doing

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the y-intercept now.

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So this just simplifies to 4y is equal to 20.

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We can divide both sides of this equation by 4 to get rid

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of this 4 right there, and you get y is equal to 20 over 4,

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which is 5.

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So when x is equal to 0, y is equal to 5.

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So the point 0, 5 is on the graph for this line.

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So 0, 5.

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x is 0 and y is 1, 2, 3, 4, 5, right over there.

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And notice, when x is 0, we're right on the y-axis, this is

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our y-intercept right over there.

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And if we graph the line, all you need is two points to

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graph any line, so we just have to connect the dots and

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that is our line.

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So let me connect the dots, trying my best to draw as

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straight of a line is I can-- well, I can do a better job

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than that-- to draw as straight of a line as I can.

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And that's the graph of this equation using the x-intercept

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and the y-intercept.

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