Question

Use the ordered pairs (3,56) and (7,85) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. If necessary round the slope to the nearest hundredth and the y intercept to the nearest whole number

Answer 1

Equation of a line in slope-intercept form:

`\begin{gathered} y=mx+b \\ \\ m\colon\text{slope} \\ b\colon y-\text{intercept} \end{gathered}`

1. Find the slope: Use two ordered pairs (x,y) in the next formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ \text{Ordered pairs (3,56) and (7,85)} \\ m=(85-56)/(7-3)=(29)/(4)=7.25 \end{gathered}`

Slope: m=7.25

2. Find the y-interept: Use one ordered pair and the slope to find b:

`\begin{gathered} \text{ordered pair: (3,56)} \\ x=3 \\ y=56 \\ \\ \text{Slope: m=7.25}_{} \\ \\ y=mx+b \\ 56=7.25(3)+b \\ 56=21.75+b \\ 56-21.75=b \\ \\ b=34.25 \\ \\ b\approx34 \end{gathered}`

y-intercept: b= 34

Then, the equation of the line is:

`y=7.25x+34`