Graph using intercepts: 2x - 5y - 10 = 0

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given the line eight X minus three. Y plus two equals zero. And we are to graph its X. And Y intercepts. And then graph the line. So how do we do that? Well we start off we recall from previous lessons that are X intercept is going to be where we plug a zero in for our Y value and then figure out what our X value is going to be for our Y intercept. Very similarly we're going to plug zero in for our X value and then see what our why value is going to be. So let's start off graphing R X intercept plugging in zero in for Y. So we'll bring down eight X minus three times not Y but zero plus two equals zero. Well negative three times zero is zero. So it's just eight X plus two equals zero. And now we can subtract two from both sides and we'll have eight X on the left equals negative two on the right. We can divide both sides by eight so we'll have X equals negative 2/8 which simplifies to negative 1/4. So our X intercept is at negative 1/4. 0. We can plot this. We have a vertical Y axis and a horizontal X axis. They meet together at the origin. And our X intercept is going to start at the origin is going to move to the left negative 1/4. So that's a very small amount, 1/4 of a unit to the left. And then it's not moving up or down at all because the Y. Value is zero. There's our X intercept. Now let's figure out our Y intercept. And again that's where we plug zero in for X. So we can put eight not times X. But zero minus three. Y plus two equals +08 times zero is zero. So we've got negative three, Y plus two equals zero. We can subtract two from both sides again and we've got negative three. Y equals negative two. We can divide both sides by negative three and we have Y equals negative two negative thirds. While those two negatives being divided cancel out. So this is two thirds. So y intercept is at 02 3rd. We plot that. Looking at our graph and starting at the origin we don't move to the left or right for our X. Because X equals zero and we go up two thirds of a unit for our Y value. And so our graph looks approximately like this. Now let's look at our answer choices and see which one matches. All right, we're looking for an X intercept at negative 1/4 0 and a Y intercept at 02 3rd. So let's see where an X intercept of negative 1/4 occurs. For answer choice A. That's negative 7/5 0. Doesn't work for answer choice B negative 1/4 0. Hey, that is what we're looking for and the Y intercept is at 02 3rd. Yes. That is exactly what we're looking for. Answer choice B. We can look and see quickly how C and D don't work because C. Has an X intercept at negative 3/4 0. That is not negative 1/4 0. An answer choice D down here is negative five halves zero, not negative 1/4 0. So yes B is the correct answer choice. Well done. We'll catch you on the next one.

Graph using intercepts: 2x - 5y - 10 = 0

Key Concepts

Intercepts

Linear Equations

Slope-Intercept Form

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