Graph the equation. (1 point) Responses Image with alt text: A line is graphed on a coordinate plane. The line passes through the points left parenthesis negative 1 comma 2 right parenthesis and left parenthesis 1 comma negative 2 right parenthesis. Image with alt text: A vertical line is graphed on a coordinate plane. The line passes through the points left parenthesis 2 comma 2 right parenthesis and left parenthesis 2 comma negative 2 right parenthesis. Image with alt text: A horizontal line is graphed on a coordinate plane. The line passes through the points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 2 comma negative 2 right parenthesis.
Since the line passes through the points (-1, 2) and (1, -2), we can find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-2 - 2) / (1 - -1) = -4/2 = -2
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Using the point (-1, 2), we can substitute the values into the equation and solve for b.
2 = -2(-1) + b
2 = 2 + b
b = 0
Therefore, the equation of the line is y = -2x + 0 or simply y = -2x.
The graph of the line passes through the points (-1, 2) and (1, -2) and is a straight line with a slope of -2.
Now, let's look at the other two images:
- The second image shows a vertical line passing through the points (2, 2) and (2, -2). This means that the x-coordinate of both points is the same, and the line is parallel to the y-axis. The equation of a vertical line is x = a, where a is the x-coordinate of any point on the line. So, in this case, the equation is x = 2.
- The third image shows a horizontal line passing through the points (-2, -2) and (2, -2). This means that the y-coordinate of both points is the same, and the line is parallel to the x-axis. The equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line. So, in this case, the equation is y = -2.
To summarize:
- The graph of the equation y = -2x is a straight line passing through the points (-1, 2) and (1, -2).
- The graph of the equation x = 2 is a vertical line passing through the points (2, 2) and (2, -2).
- The graph of the equation y = -2 is a horizontal line passing through the points (-2, -2) and (2, -2).