Graphing lines using x and y intercepts
X and Y intercepts X and Y intercepts
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- 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 5.
- 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.
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