Question

which equation represents the relationship between the x - values and the y - values in the table?

x	y
5	55
10	105
15	155
20	205

a) $y = 11x$
b) $y = 10x + 5$
c) $y = x + 5$
d) $y = 5x + 5$

Explanation:

Step1: Identify the form of the equation

The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We can find \( b \) by looking at the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 5 \), so \( b = 5 \).

Step2: Calculate the slope \( m \)

The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points, for example, \( (x_1,y_1)=(0,5) \) and \( (x_2,y_2)=(5,55) \). Then \( m=\frac{55 - 5}{5 - 0}=\frac{50}{5} = 10 \).

Step3: Form the equation

Using the slope - intercept form \( y=mx + b \), with \( m = 10 \) and \( b = 5 \), the equation is \( y=10x + 5 \).

Answer:

B. \( y = 10x+5 \)