To find the equation in slope-intercept form (y = mx + b) from the given points, we'll first identify the points from the table based on the values you've provided:
x | y
---------
-2 | -7
-1 | -4
0 | -1
1 | 2
2 | 5
Next, we'll use two points to find the slope (m) of the line. Let's use the points (0, -1) and (1, 2):
- Calculate the slope (m):
The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using (0, -1) as (x₁, y₁) and (1, 2) as (x₂, y₂): \[ m = \frac{2 - (-1)}{1 - 0} = \frac{2 + 1}{1} = \frac{3}{1} = 3 \]
- Use the slope and one point to find the y-intercept (b):
We can use the point (0, -1) to find b: \[ y = mx + b \] Substituting in the values from the point (0, -1): \[ -1 = 3(0) + b \implies -1 = b \]
- Write the equation:
Now that we have the slope and the y-intercept, we can write the equation: \[ y = 3x - 1 \]
Thus, the equation in slope-intercept form is: \[ y = 3x - 1 \]