Question

Write an equation that represents the function (1,34) (2,56) (3,78) (4,100) and explain how you found your equation.

A) y = 22x + 12
B) y = 22x - 12
C) y = 12x + 22
D) y = 12x - 22

Answer 1

The equation that represents the function is y = 22x + 12. The slope, using two points, is found to be 22. The y-intercept is then determined to be 12 by substituting the slope and a point into the slope-intercept form equation.

Step-by-step explanation:

To find the equation that represents the given function, we need to determine the equation of the line that passes through the given points. We can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, find the slope of the line using the formula m = (y2 - y1) / (x2 - x1) with any two of the given points. Let's use (1, 34) and (2, 56). Plugging the values into the formula, we get m = (56 - 34) / (2 - 1) = 22.

Next, substitute the slope m and one of the points (let's use (1, 34)) into the slope-intercept form equation and solve for b. We have 34 = 22(1) + b. Solving for b, we get b = 12.

Therefore, the equation that represents the given function is y = 22x + 12. The correct answer is A) y = 22x + 12.