Essentially, we are going to reverse graph, meaning we are given a graph and are to find its equation. Instead of graphing the equation, we are given the graph and must find the correct equation; therefore, we need to use the graph’s information to fill in the equation’s variables.
1.) Read through the questions and interpret what it means. Ask yourself, what is the slope and y-intercept and how do I find them? What is slope-intercept form and how do I input this information into it?
2.) First, recall slope-intercept form, slope, and y-interception. The name “slope-intercept” means the equation form with the slope and y-intercept, hence, “slope-intercept.” Remember, anytime you hear this, decode it to slope and y-intercept. So, you know that slope-intercept is in the form: y=mx+b. With this, m=slope, and b=y-intercept. More specifically, the slope (m) is ratio of rise over run of the graph, so m=rise/run. The y-intercept is the starting point and where the graph intercepts the y-axis.
3.) So, we need to find the slope and y-intercept to use y=mx+b, since this is the required information in this form to graph the equation.
• m(slope) formula = y2-y1/x2-x1
- This formula is the difference of y-values over the difference of x-values, which simplifies to vertical change/lateral change or rise/run.
4.) Pick two coordinate pairs, so we can use the slope formula. Remember, two coordinate pairs looks like: (x1, y1) and (x2, y2).
The points (0,4) and (6, 2) are exact intercepts, meaning they intercept the coordinates exactly, so they don’t contain decimals or fractions.
5.) Input these points into the slope formula:
• m=(2)-(4)/(6)-(0)
- note that parenthesis are used when substituting in for a variable.
• m=-2/6
- remember to simplify the slope to a unit rate.
• m=-1/3
So, the graph goes down 1 unit and over 3 units.
6.) To find the y-intercept, we can look at the graph and see where it intercepts the y-axis, or substitute in x=0. Both methods will tell us that b=4.
7.) Input m and b into y=mx+b:
y=(-1/3)x+(4); m=-1/3 and b=4