In the graph shown, identify the $y$–intercept & slope. Write the equation of this line in Slope-Intercept form.

• A. $y=\(\frac\)23x+1$
• B. $y=-\(\frac\)23x+1$
• C. $y=-2x+1$
• D. $y=x+2$

Answer: (B)

Verified step by step guidance

1. Identify the y-intercept by looking at the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at \(y = 1\).
2. Determine the slope by finding two points on the line. For example, use the points \((0, 1)\) (the y-intercept) and \((3, -1)\).
3. Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substitute the points: \(m = \frac{-1 - 1}{3 - 0} = \frac{-2}{3}\).
4. Write the equation of the line in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
5. Substitute the slope and y-intercept values into the equation: \(y = -\frac{2}{3}x + 1\).