Graph the equation 9- =3/2t using slope-intercept form
First, let's rearrange the equation to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Given equation: 9 - = (3/2)t
To isolate the variable t, subtract 9 from both sides: - = (3/2)t - 9
Next, divide both sides by (3/2) to solve for t: - / (3/2) = (3/2)t - 9 / (3/2)
Simplifying further: - * (2/3) = (3/2)t - (9 * 2) / 3
- * (2/3) = (3/2)t - 18/3
- = (3/2)t - 6
Now we have the equation in slope-intercept form: y = (3/2)t - 6
Since we do not have a specific value for y, we can assign it any value we want and solve for t. Let's assign different values to y and find the corresponding values of t to create a table.
Let y = 0, then the equation becomes:
0 = (3/2)t - 6
(3/2)t = 6
t = (6 * 2)/3
t = 4
Let y = 3, then the equation becomes:
3 = (3/2)t - 6
(3/2)t = 6 + 3
(3/2)t = 9
t = (9 * 2)/3
t = 6
Let y = -3, then the equation becomes:
-3 = (3/2)t - 6
(3/2)t = 6 - 3
(3/2)t = 3
t = (3 * 2)/3
t = 2
Now, let's plot these points on a graph and draw a line through them:
Point 1: (4, 0)
Point 2: (6, 3)
Point 3: (2, -3)
Here is the graph:
*[illustration graph_9_minus_.png]