Answer:
See the image for the actual graph (below I will give an explanation)
Skills needed: Graphing, Slope Intercept Form
Step-by-step explanation:
1) The form that we have here is known as slope intercept form.
---> [tex]y=mx+b[/tex]
In this form, [tex]y[/tex] is the y-coordinate value, [tex]m[/tex] is the slope, [tex]x[/tex] is the x-coordinate value, and [tex]b[/tex] is the y-intercept.
2) In this scenario:
- [tex]\frac{1}{4} \text{ is the slope or m}[/tex]
- [tex]\text{x is x}[/tex]
- [tex]\text{-1 is b}[/tex]
3) The y intercept (or [tex]b[/tex]), is what y equals when x equals 0.
So the coordinate pair is [tex](0,b)[/tex] given some value of [tex]b[/tex] from the equation.
In this situation: [tex]b=-1, (0,-1) \text{ is the coordinate point}[/tex]
4) So we can plot a point at (0,-1), which is one unit below the origin (the absolute center of the coordinate plane -- (0,0) )
5) Now, we need to understand what slope is.
Slope = [tex]\frac{\text{change of y}}{\text{change of x}}[/tex]
In this case, we got [tex]\frac{1}{4}[/tex], so that means every time the y coordinate changes by 1, the x coordinate changes by 4. This means that when we go up 1 (increasing the y coordinate by 1), we have to go right 4 (increasing the x coordinate by 4).
Also, every time we go down (decreasing the y coordinate by 1), we have to go left 4 (decreasing the x coordinate by 4).
Therefore, we can go up 1, right 4 from the y intercept as many times as possible (so plot all the points that fit like that). Then, we can go down 1, left 4 from the y-intercept as many times as possible (plot all that fit).
6) That's about it for the graph. Now connect all those points and you are good to go. Hope you understood (check the image for details).
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