The guided three-step process is designed to help you calculate slope and y-intercept from a pair of points.
Define the linear function through (-2,5) and (3,-10).
Step 1: Calculate the slope of the line by replacing the variables in the equation below with their corresponding coordinates.
$$\displaystyle slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\qquad-\qquad}{\qquad-\qquad} = \frac{\qquad}{\qquad}$$ Hint: 𝑦2 = - 10
Step 2: Use the slope intercept form of the line to calculate the y-intercept.
-
replace 𝑚 with the slope we just calculated
-
replace 𝑥 and 𝑦 with the values from the first point: ( - 2,5)
-
solve for 𝑏
Slope-intercept form of the line: 𝑦 = 𝑚𝑥 + 𝑏
= + 𝑏
= 𝑏
*Note*: We could also have done Step 2 using the second point: (3, - 10). Let’s do that now to make sure we get the same result!
= + 𝑏
= 𝑏
Step 3: Use the slope and y-intercept we calculated to write our function definition!
𝑓(𝑥) = 𝑥 +
Define the linear function through (-5,2) and (3,6).
Step 1: Calculate slope.
$$\displaystyle slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\qquad-\qquad}{\qquad-\qquad} = \frac{\qquad}{\qquad}$$
Step 2: Calculate the y-intercept. Hint: You can use either point. Which would be simpler?
= 𝑏
Step 3: Write the function definition!
𝑓(𝑥) = 𝑥 +
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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