Select the graph for this equation by using slope-intercept form.
The Correct Answer and Explanation is:
To select the correct graph for the equation 2x + y = 1, it is essential to first convert the equation into slope-intercept form, which is written as y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept, which is the point where the line crosses the vertical y-axis.
Step 1: Convert the equation to slope-intercept form.
The given equation is 2x + y = 1. To transform this into the y = mx + b format, the variable y must be isolated on one side of the equation. This is achieved by subtracting 2x from both sides of the equation:
2x – 2x + y = 1 – 2x
y = -2x + 1
Now the equation is in slope-intercept form.
Step 2: Identify the slope (m) and the y-intercept (b).
By comparing y = -2x + 1 to the general form y = mx + b, the following values can be identified:
- The y-intercept (b) is 1. This means the line will cross the y-axis at the point (0, 1).
- The slope (m) is -2. The slope indicates the steepness and direction of the line. It can be expressed as a fraction, m = -2/1, which represents the “rise over run.”
Step 3: Use the y-intercept and slope to find points on the graph.
- Plot the y-intercept: Begin by locating the y-intercept on the coordinate plane. Since b = 1, the first point is at (0, 1).
- Apply the slope: The slope m = -2/1 provides directions to find a second point. The “rise” is -2, which means moving 2 units down. The “run” is 1, which means moving 1 unit to the right. Starting from the y-intercept (0, 1), move 2 units down and 1 unit to the right. This brings you to the point (1, -1).
The correct graph is a straight line that passes through the points (0, 1) and (1, -1). It will be a downward-sloping line that crosses the y-axis at a positive value.
