Question

What is the equation of the graph below?

Answer 1

Answer:

-2x+y=8

Step-by-step explanation:

First, change the equations into slope-intercept form. See the attached image for how to change the equations into slope-intercept form (if you have any questions on how to do this, let me know in the comments!)

Remember that b is the y-intercept. The y-intercept in the graph is 8, so the answer has to be an equation ending with 8 as the b.

This leaves us with 2x+y=8 and -2x+y=8 (their slope-intercept form is y=-2x+8 and y=2x+8, respectively) as our only options.

Then, we have to find the equation with a slope, which is m, that matches the slope of the graph.

We can figure out the graph's slope by using the $\frac{y_2-y_1}{x_2-x_1}$ formula.

We need two points on the graph to find the slope. We can use (0,8) and (-4,0) for this.

We need to input the coordinates into the formula. Make sure the order of each y and x match up with the coordinates (ex: you can do $\frac{y_2-y_1}{x_2-x_1}$ and $\frac{y_1-y_2}{x_1-x_2}$, but you cannot do $\frac{y_1-y_2}{x_2-x_1}$ or $\frac{y_2-y_1}{x_1-x_2}$).

Let's do $\frac{0-8}{-4-0}$, which becomes $\frac{-8}{-4}$. This simplifies to $\frac{2}{1}$, which becomes 2. Thus, our answer needs to have a slope of 2.

Again, our options are 2x+y=8 and -2x+y=8 (their slope-intercept form is y=-2x+8 and y=2x+8, respectively). Looking at their slope-intercept form, the second equation, y=2x+8 is the one with the slope of 2 (the other has a slope of -2). Thus, -2x+y=8 is your answer!

Hope that helps! <3

Disclaimer: I am not responsible for anything you get incorrect, as I only have the context and information you provide, and I give my response based on my knowledge supported with credible information from experts and online professional articles.

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Answer 2

Answer:

-2x+y=8

Step-by-step explanation:

In slope-intercept form -2x+y=8 is y=2x+8.

After converting, it is easier to graph.

The constant 8 is the y intercept.

The slope is 2.

Knowing these values, one will find (0,8).

From that coordinate one will go up 2 right one then down 2 left 1 till the graph is complete.