Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts. Provide an example to support your response.

When graphing a linear equation using the x and y intercepts, we first need to be familiar with what the x-intercept is, and what the y-intercept is. The x-intercept of the graph of a function, or linear equation is the point where the graph crosses the x axis, whereas the y-intercept is the point when the graph crosses the y axis. Only one line can be drawn through two points that are given. So if we know the intercepts we can draw a line, or graph the line. Therefore, we graph a linear equation by finding the intercepts by solving for x, then solving for y, or vise versa.
For example if I wanted to find and graph the x, and y intercept of the linear equation: 4x+6y=24
I would first solve for y by letting x=o, such as: 4(0) +6y=24
6y=24
Y=4
So, the y intercept is (0, 4)
Now, to find the x intercept we do the same as we did for finding why, but instead of letting x=o, we let y=0
4x+6(0) =24
4x+6(0) =24
4x=24
X=6
So, the x intercept is (6, 0)
Now that we have the points we can graph
For the x-intercept we first move to the right 6 times and because the second point is a zero, we plot on the line. Now to plot the y-intercept, we start at zero and stay because that is our first point, then to plot the second point we move by four and plot. Now we graph y drawing a straight line through the two given points. To check if this is correct, it is a good thing to solve by using a third point to check. I will use 3 in the place for x and solve for y.
4(3) +6y=24
12+6y=24
6y=24-12
6y=12
Y=2
So, the next set we plot will be (3,2): we move to the right 3 times and up 2 and plot, then graph by drawing a line through this point.
This set of points is on the line.

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