Final answer:
The equation of the linear function with a slope of -56 and passing through the point (9, 112) is y = -56x + 616. This was determined by substituting the given point into the slope-intercept form of a linear equation and solving for the y-intercept. The validity of this equation was confirmed by re-substituting the point into the equation.
Step-by-step explanation:
The student is looking to write the equation of a linear function that passes through a specific point (9, 112) and has a given slope of -56. The general form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept.
- First, we will find the b-value through substitution. Given the point (9, 112) and the slope (-56), we substitute these into the equation, resulting in 112 = -56(9) + b. Solving this, we find that b = 112 + 504, which simplifies to b = 616.
- Next, we will write the equation of the line with the slope and y-intercept we've found, which is y = -56x + 616.
- To check the equation, we substitute the x-value from the given point into the equation to see if we get the correct y-value: y = -56(9) + 616, yielding y = -504 + 616 which simplifies to y = 112, which is the same as the y-value of our point, confirming the equation is correct.
Therefore, the equation of the line is y = -56x + 616, which we have verified by substitution.