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

• A. $y=\frac23x+1$
• B. $y=-\frac23x+1$
• C. $y=-2x+1$
• D. $y=x+2$

Answer: (B)

Verified step by step guidance

1. First, identify the y-intercept of the line on the graph. The y-intercept is the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at y = 1.
2. Next, determine the slope of the line. The slope is calculated as the change in y divided by the change in x between two points on the line. Choose two points on the line, such as (0, 1) and (3, -1).
3. Calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1). Substitute the chosen points into the formula: slope = (-1 - 1) / (3 - 0) = -2/3.
4. Now, 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. Substitute the slope and y-intercept into the equation: y = -2/3x + 1.
5. Verify the equation by checking if other points on the line satisfy the equation. For example, check if the point (3, -1) satisfies the equation: y = -2/3(3) + 1 = -2 + 1 = -1, which is correct.