Question

use the graph to answer the question. if point (x,27) lies on the line shown on the graph, what is the valu type only the number in the box

Explanation:

Step1: Find the slope of the line

We have two points \((0, 5)\) and \((6, 7)\). The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values, we get \(m=\frac{7 - 5}{6 - 0}=\frac{2}{6}=\frac{1}{3}\).

Step2: Find the equation of the line

Using the slope - intercept form \(y = mx + b\), where \(b\) is the \(y\) - intercept. From the point \((0,5)\), we know that \(b = 5\). So the equation of the line is \(y=\frac{1}{3}x + 5\).

Step3: Solve for \(x\) when \(y = 27\)

Substitute \(y = 27\) into the equation \(y=\frac{1}{3}x+5\):
\[

$$\begin{align*} 27&=\frac{1}{3}x + 5\\ 27-5&=\frac{1}{3}x\\ 22&=\frac{1}{3}x\\ x&=22\times3\\ x& = 66 \end{align*}$$

\]

Answer:

66