Find the xx and yy-intercepts of the line x4−y3=1\frac{x}{4}-\frac{y}{3}=1.

x − i n t : ( 4 , 0 ) x-int:\left(4,0\right) x − in t : ( 4 , 0 ) y − i n t : ( 0 , − 3 ) y-int:\left(0,-3\right) y − in t : ( 0 , − 3 )

Find the x x and y y -intercepts of the line x 4 − y 3 = 1 \frac{x}{4}-\frac{y}{3}=1 .

We have a problem that asks us to find the x and y intercepts of the line x over four minus y over three equals one. Now this problem looks a little more complicated because we have this situation where there are fractions in this equation, but it turns out solving this is pretty straightforward to what we already know. So we're looking for the x intercepts, and we're looking for the y intercept. Now remember the way that we can find this is by setting the other variable to zero. So if we're finding the x intercept, we set y equal to zero. And if we're looking for the y intercept, we set x equal to zero. So let's first start by finding the x intercept. Well, that means setting y equal to zero. So for this equation here, we're going to have x over four minus, and I'm gonna set that y equal to zero, so zero over three equals one. Now zero divided by three just ends up being zero, so that means we're going to have x over four minus zero is equal to one. Now x over four minus zero, that's the same thing as just x over four. If we want to solve this, I can take that four and multiply it on both sides of this equation. That'll cancel the fours, isolating just x, and one times four is four. So our x value is going to be four. And since I know my y value is zero, that will give us the point four comma zero, and this right here would be the x intercept. Now I need to find the y intercept. For the y intercept, we wanna set x equal to zero. So using this same equation, we're going to have zero over four minus y over three is equal to one. Now I'm gonna skip a couple steps here because I know that zero over four will give us zero, and zero minus y over three is just gonna be negative y over three. So skipping these steps will go to negative y over three, and that equals one. Right? Because we just need to think about what happens if we subtract y over three from zero. So that gives us this. Now what I want to do from here is I want to get y by itself. I can't just multiply three on both sides because we'll still have a negative sign in front of y. So what I need to do is multiply both sides by negative three. If we multiply both sides by negative three, that'll cancel the negative signs, because remember, a negative times a negative gives you a positive, and that'll also cancel the three in the numerator and denominator. So since the negative signs are gone and the threes are gone, what does that leave us with on the left side? Well, only y. And one times negative three is negative three. So we get a y value of negative three, and we know our x value is zero, so we get an x of zero and a y of negative three, and that right there would be our point and the y intercept. So this is how you can find the x and y intercepts for the line that we have up here. Hope you found this video helpful. See you in the next one.

Find the x x and y y -intercepts of the line x 4 − y 3 = 1 \frac{x}{4}-\frac{y}{3}=1 .

x − i n t : ( 4 , 0 ) x-int:\left(4,0\right) x − in t : ( 4 , 0 ) y − i n t : ( 0 , − 3 ) y-int:\left(0,-3\right) y − in t : ( 0 , − 3 )

x − i n t : ( 4 , 0 ) x-int:\left(4,0\right) x − in t : ( 4 , 0 ) y − i n t : ( 0 , 3 ) y-int:\left(0,3\right) y − in t : ( 0 , 3 )

x − i n t : ( − 4 , 0 ) x-int:\left(-4,0\right) x − in t : ( − 4 , 0 ) y − i n t : ( 0 , 3 ) y-int:\left(0,3\right) y − in t : ( 0 , 3 )

x − i n t : ( − 4 , 0 ) x-int:\left(-4,0\right) x − in t : ( − 4 , 0 ) y − i n t : ( 0 , − 3 ) y-int:\left(0,-3\right) y − in t : ( 0 , − 3 )

4. Graphs and Functions

Graph Linear Equations Using Intercepts

Intermediate Algebra

4. Graphs and Functions

Graph Linear Equations Using Intercepts

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Multiple Choice

Find the $x$ and $y$ -intercepts of the line $\frac{x}{4} - \frac{y}{3} = 1$ .

$x-int:\left(4,0\right)$

$y-int:\left(0,3\right)$

$x-int:\left(4,0\right)$

$y-int:\left(0,-3\right)$

$x-int:\left(-4,0\right)$

$y-int:\left(0,3\right)$

$x-int:\left(-4,0\right)$

$y-int:\left(0,-3\right)$

Verified step by step guidance

To find the x-intercept, set y = 0 in the equation $\frac{x}{4} - \frac{y}{3} = 1$. This is because the x-intercept occurs where the graph crosses the x-axis, and at this point, the y-coordinate is zero.

Substitute y = 0 into the equation to get $\frac{x}{4} - \frac{0}{3} = 1$, which simplifies to $\frac{x}{4} = 1$.

Solve for x by multiplying both sides of the equation by 4: $x = 4$.

To find the y-intercept, set x = 0 in the original equation $\frac{x}{4} - \frac{y}{3} = 1$. The y-intercept occurs where the graph crosses the y-axis, so the x-coordinate is zero at this point.

Substitute x = 0 into the equation to get $\frac{0}{4} - \frac{y}{3} = 1$, which simplifies to $-\frac{y}{3} = 1$. Then solve for y by multiplying both sides by -3: $y = -3$.

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