Define the linear function through (-2,5) and (3,-10).
Start by assigning values for x1, y1, x2, y2 from the coordinates above: -2x1 y1 x2 y2
Step 1: Calculate the slope of the line by replacing the variables in the equation below with their corresponding coordinates.
$$\displaystyle slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\qquad-\qquad}{\qquad-\qquad} = \frac{\qquad}{\qquad}$$
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).
Start by assigning values for x1, y1, x2, y2 from the coordinates above: x1 y1 x2 y2
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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