The image shows two tables of data, with the corresponding linear functions and their rates of change and y-intercepts.
Table 1
| X | Y |
| 0 | -1 |
| 1 | 4 |
| 2 | 9 |
| 3 | 14 |
| 4 | 19 |
Linear function: y = 5x - 1
Rate of change: 5
Y-intercept: -1
Table 2
| X | Y |
| 0 | 4 |
| 1 | 1.5 |
| 2 | -1 |
| 3 | -3.5 |
| 4 | -6 |
Linear function: y = -2.5x + 4
Rate of change: -2.5
Y-intercept: 4
To graph the linear functions, we can use the slope-intercept form of the equation: y = mx + b, where m is the slope and b is the y-intercept
To find the slope, we can use the following formula:
slope = (y2 - y1) / (x2 - x1)
For example, to find the slope of the line in Table 1, we can use the following points:
(0, -1) and (1, 9)
slope = (9 - -1) / (1 - 0) = 10
Therefore, the slope of the line in Table 1 is 10.
To find the y-intercept, we can substitute any point from the table into the equation. For example, we can use the point (0, -1):
y = mx + b
-1 = 23 * 0 + b
b = -1
Therefore, the y-intercept of the line in Table 1 is -1.
We can follow the same steps to find the slope and y-intercept of the line in Table 2. The slope of the line in Table 2 is -2.5 and the y-intercept is 4.