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 +

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