Q23. - Algebra 2

Question

Which line best fits the data in the graph at the right?

$\begin{array}{l}A)y=x\\ B)y=-0.5x+4\\ C)y=-0.5x-4\\ D)y=0.5+0.5x\end{array}$

Step-by-Step Solution

Answer

The correct option is $D) 0.5+0.5x$.

Step-1 – Determine the points.

The coordinates of the points are $(1,0.5),(2,1.5),(3,2),(4,2.5)$

Step-2 – Calculate the slope of the line.

The slope is positive so all options with negative slope must be incorrect.

Take any two points and determine the equation except the points $(1,0.5)$.

Let the points are $(2,1.5) and (3,2)$.

Substitute $\left(x_1{y}_1\right)=(2,1.5) and \left(x_2{y}_2\right)= (3,2)$ into the formula $slope=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}m=\frac{2-1.5}{3-2}\\ m=0.5\end{array}$

Step-3 – Make the equation.

Substitute $\left(x_1{y}_1\right)=(2,1.5)$ into $y-y_1=m(x-x_1)$.

 $\begin{array}{l}y-1.5=0.5(x-2)\\ y-1.5=0.5x-1\\ y=0.5x+0.5\end{array}$

From the given options the only possible match can be option $D) 0.5+0.5x$.

Thus, the line best fits the data in the graph should be $D) 0.5+0.5x$.