Final answer:
To write a linear function with the given values, use the slope-intercept form of a linear equation. Find the slope using the formula (y2 - y1) / (x2 - x1), substitute the slope and a point into the slope-intercept form, and simplify to get the linear function.
Step-by-step explanation:
To write a linear function with the given values, we need to find the equation of the line passing through the points (1, 1) and (-3, 17). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (1, 1) and (-3, 17), we get m = (17 - 1) / (-3 - 1) = 4.
Next, we choose one of the points (1, 1) and substitute the coordinates and the slope into the slope-intercept form. Using the point-slope form, the equation becomes y - y1 = m(x - x1), which gives us y - 1 = 4(x - 1). Simplifying it further, we get y = 4x - 3.
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