Answer:
To find the equation of the graphed line, we need to identify its slope and y-intercept. The slope is the ratio of the vertical change to the horizontal change between any two points on the line. The y-intercept is the point where the line crosses the y-axis.
Looking at the image, we can see that the line passes through the points (-3, 4) and (3, -2). We can use these points to calculate the slope:
slope = (y2 - y1) / (x2 - x1) slope = (-2 - 4) / (3 - (-3)) slope = -6 / 6 slope = -1
The slope of the line is -1. This means that for every unit increase in x, the y value decreases by 1 unit.
To find the y-intercept, we can use either of the points and plug them into the equation y = mx + b, where m is the slope and b is the y-intercept. For example, using the point (-3, 4), we have:
4 = -1 * (-3) + b 4 = 3 + b b = 1
The y-intercept of the line is 1. This means that the line crosses the y-axis at (0, 1).
Therefore, the equation of the graphed line is:
y = -x + 1
This equation matches with one of the options given below the graph: y = -1/2x + 4. This is because we can multiply both sides of the equation by 2 and get:
2y = -2x + 2 y = -1/2x + 4
Answer: The equation that describes the graphed line is y = -1/2x + 4.