I'll work through each problem step by step to find the correct equations for the given graphs.
Problem 1:
Looking at the graph, I need to identify the slope and y-intercept.
- The line passes through (0, 3), so the y-intercept is 3
- The line appears to have a slope of 2 (rises 2 units for every 1 unit it moves right)
- Using slope-intercept form: y = mx + b, where m = 2 and b = 3
- Equation: y = 2x + 3
Answer: (iv) y = 2x + 3
Problem 2:
Analyzing this graph:
- The line passes through (0, -8), so the y-intercept is -8
- The slope appears to be -2 (goes down 2 units for every 1 unit right)
- Equation: y = -2x - 8
Answer: (i) y = -2x - 8
Problem 3:
For this graph:
- The line passes through (0, 4), so the y-intercept is 4
- The slope is negative, going down 2 units for every 1 unit right
- Slope = -2
- Equation: y = -2x + 4
Answer: (ii) y = -2x + 4
Problem 4:
Examining this graph:
- The line passes through (0, -3), so the y-intercept is -3
- The slope is positive and steep, rising 7 units for every 1 unit right
- Slope = 7
- Equation: y = 7x - 3
Answer: (i) y = 7x - 3
Problem 5:
For this final graph:
- The line passes through (0, -4), so the y-intercept is -4
- The slope is positive and very steep, rising 5 units for every 1 unit right
- Slope = 5
- Equation: y = 5x - 4
Answer: (iv) y = 5x - 4
Final Answer:
1) (iv) y = 2x + 3
2) (i) y = -2x - 8
3) (ii) y = -2x + 4
4) (i) y = 7x - 3
5) (iv) y = 5x - 4
Parent Tip: Review the logic above to help your child master the concept of worksheet for graphing linear equations.
