The Correct Answer and Explanation is:
Correct Answer:
y = -2/3x + 2
Explanation:
To find the equation of the line, we can use the slope-intercept form, which is y = mx + b. In this formula, ‘m’ represents the slope of the line, and ‘b’ represents the y-intercept. The process involves finding these two values from the provided graph.
First, we identify the y-intercept, ‘b’. This is the point where the line crosses the vertical y-axis. By examining the graph, we can see the line intersects the y-axis at the point (0, 2). Therefore, the value of the y-intercept, b, is 2.
Next, we need to calculate the slope, ‘m’. The slope is a measure of the line’s steepness and is defined as the ‘rise’ (vertical change) divided by the ‘run’ (horizontal change) between any two points on the line. We can use the two labeled points, A at (-2, 3) and B at (4, -1), to calculate this.
Using the slope formula, m = (y2 – y1) / (x2 – x1), we substitute the coordinates of points A and B:
m = (-1 – 3) / (4 – (-2))
m = -4 / (4 + 2)
m = -4 / 6
This fraction simplifies to -2/3. So, the slope ‘m’ is -2/3.
Alternatively, we can find the slope by counting units on the grid. Starting from a clear point like the y-intercept (0, 2), we can observe that to get to the next clear point at (3, 0), we must move down 2 units (a rise of -2) and to the right 3 units (a run of +3). This gives a slope of rise over run, or -2/3, confirming our calculation.
With both the slope and y-intercept identified, we can now write the final equation. We substitute m = -2/3 and b = 2 into the slope-intercept format y = mx + b. This gives us the complete equation for the line.
