Question

the line $y = \frac{7}{3}x + 7$ is graphed
match each graph characteristic with its value

Explanation:

The equation of the line is given in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step1: Identify the y - intercept

In the equation \(y=\frac{7}{3}x + 7\), when \(x = 0\), \(y=b\). So the y - intercept \(b = 7\). This is the value of \(y\) when the line crosses the \(y\) - axis.

Step2: Identify the slope

In the equation \(y=\frac{7}{3}x + 7\), the coefficient of \(x\) is the slope \(m\). So the slope \(m=\frac{7}{3}\). The slope represents the rate of change of \(y\) with respect to \(x\) (rise over run).

Step3: Find the x - intercept

To find the x - intercept, we set \(y = 0\) in the equation \(y=\frac{7}{3}x+7\).
\[

$$\begin{align*} 0&=\frac{7}{3}x + 7\\ \frac{7}{3}x&=- 7\\ x&=-7\times\frac{3}{7}\\ x&=- 3 \end{align*}$$

\]
The x - intercept is the value of \(x\) when the line crosses the \(x\) - axis, so the x - intercept is \(-3\).

If we assume the characteristics are y - intercept, slope, and x - intercept:

• Y - intercept: \(7\)
• Slope: \(\frac{7}{3}\)
• X - intercept: \(-3\)

Answer:

• Y - intercept: \(7\)
• Slope: \(\frac{7}{3}\)
• X - intercept: \(-3\)