The relationship between two variables, x and y, is linear. For every increase in the value of x by 1, the value of y increases by 8. When the value of x is 2, the value of y is 18. Which equation represents this relationship?

Explanation

Choice C is correct. It's given that the relationship between x and y is linear. An equation representing a linear relationship can be written in the form y = mx + b, where m is the slope and b is the y-coordinate of the y-intercept of the graph of the relationship in the xy-plane. It's given that for every increase in the value of x by 1, the value of y increases by 8. The slope of a line can be expressed as the change in y over the change in x. Thus, the slope, m, of the line representing this relationship can be expressed as 8/1, or 8. Substituting 8 for m in the equation y = mx + b yields y = 8x + b. It's also given that when the value of x is 2, the value of y is 18. Substituting 2 for x and 18 for y in the equation y = 8x + b yields 18 = 8(2) + b, or 18= 16 + b. Subtracting 16 from each side of this equation yields 2=b. Substituting 2 for b in the equation y = 8x + b yields y = 8x + 2. Therefore, the equation y = 8x + 2 represents this relationship.