Answer:
y = -2.5x + 13
Explanation:
Harper made a few errors while attempting to write the equation of the linear function. Firstly, Harper incorrectly subtracted f(6) from f(2) instead of subtracting the corresponding y-coordinates of the two points. Secondly, the values obtained for the change in y and change in x were flipped, resulting in the wrong slope. Lastly, Harper made an arithmetic error while calculating the slope.
To write the equation of a linear function in slope-intercept form, we need to find the slope of the line and the y-intercept. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points are (2, 8) and (6, -2). Therefore,
slope = (-2 - 8) / (6 - 2) = -10 / 4 = -2.5
Now, to find the y-intercept, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (2, 8) and the slope we just calculated, we get:
y - 8 = -2.5(x - 2)
Expanding and simplifying, we get the equation of the linear function in slope-intercept form:
y = -2.5x + 13
Therefore, Harper's equation for the linear function in slope-intercept form should have been y = -2.5x + 13
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