The Correct Answer and Explanation is:
- Equation: y = 3x + 1
- This equation is in slope-intercept form: y = mx + b, where the slope (m) is 3 and the y-intercept (b) is 1. Starting at the point (0,1) on the y-axis, move up 3 units and right 1 unit for each subsequent point. The graph will intersect with the letter X.
- Equation: y = x – 3
- This equation has a slope of 1 (since there’s no number in front of x, it’s implicitly 1) and a y-intercept of -3. Starting at (0,-3), plot a point. The graph intersects with the letter X.
- Equation: y = -3x + 2
- This equation has a slope of -3, indicating the line will go down 3 units for every 1 unit to the right. Starting at (0,2), the graph intersects at X.
- Equation: y = 2x – 4
- The slope is 2, and the y-intercept is -4. Starting at (0,-4), the graph intersects at B.
- Equation: y = -3x – 1
- The slope is -3, and the y-intercept is -1. Starting at (0,-1), the graph intersects at F.
- Equation: y = 2x + 3
- The slope is 2, and the y-intercept is 3. Starting at (0,3), the graph intersects at I.
- Equation: y = 4x – 2
- The slope is 4, and the y-intercept is -2. Starting at (0,-2), the graph intersects at L.
- Equation: y = -1/4x + 2
- The slope is -1/4, and the y-intercept is 2. Starting at (0,2), the graph intersects at D.
- Equation: y = 5/3x
- The slope is 5/3, and there’s no y-intercept since it’s 0. Starting at the origin (0,0), the graph intersects at A.
In conclusion, each equation’s graph intersects a specific letter on the grid. You can graph the lines by plotting the y-intercept and using the slope to plot additional points, drawing a straight line through them.
