Question

The table below represents the number of paintings, y, that Jordan completed in x years. Jordan's Paintings Year (x) Paintings (y) 1 4 2 7 3 10 4 13 Which equation describes the relmionship between the number of paintings and the year? A. y = x+3 B. y = 3x + 1 D.y = 4x + 3 C. y = 3x + 4

Answer 1

Method 1

Concept

Pick two points and find the equation of a line.

Point ( 1. 4 ) and ( 2, 7 )

Step 2: Represent each point

`\begin{gathered} x_1\text{ = 1} \\ y_1\text{ = 4} \\ x_2\text{ = 2} \\ y_2\text{ = 7} \end{gathered}`

Step 3: Substitute the values in the two points equation of a line formula

`(y-y_1)/(x-x_1)\text{ = }(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{7\text{ - 4}}{2\text{ - 1}} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }(3)/(1) \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = 3} \\ \text{Cross multiply} \\ y\text{ - 4 = 3(x - 1)} \\ y\text{ - 4 = 3x - 3} \\ y\text{ = 3x - 3 + 4} \\ y\text{ = 3x + 1} \end{gathered}`

Step 4: Final answer

y = 3x + 1 Option B