To find the linear function in slope-intercept form (y = mx + b) that corresponds to the points given, we first need to determine the slope (m) and then find the y-intercept (b).
Step 1: Calculate the Slope (m)
The slope (m) can be calculated using any two points on the line. We will use the points (-2, -3) and (0, 1).
The formula for the slope (m) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (-2, -3) as (x₁, y₁) and (0, 1) as (x₂, y₂):
\[ m = \frac{1 - (-3)}{0 - (-2)} = \frac{1 + 3}{0 + 2} = \frac{4}{2} = 2 \]
Step 2: Find the y-intercept (b)
Now that we have the slope, we can use any point to find the y-intercept (b). Let's use the point (0, 1):
Using the equation of the line:
\[ y = mx + b \]
Substituting in the values for (x, y) = (0, 1) and m = 2:
\[ 1 = 2(0) + b \]
This simplifies to:
\[ 1 = 0 + b \]
Thus, the y-intercept is \( b = 1 \).
Step 3: Write the equation
Now we have both the slope and the y-intercept:
- Slope (m) = 2
- Y-intercept (b) = 1
So the equation of the line in slope-intercept form is:
\[ y = 2x + 1 \]
Final answer
The answer is: \[ y = 2x + 1 \]
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