Let’s solve each problem one by one. We’re graphing lines given in slope-intercept form:
y = mx + b, where:
-
m is the slope (rise over run)
-
b is the y-intercept (where the line crosses the y-axis)
We’ll find two points for each line and draw a straight line through them.
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Problem 1: y = -¹/₅x – 2
- Y-intercept: when x=0, y = -2 → point (0, -2)
- Slope = -1/5 → go down 1, right 5 from (0,-2) → next point: (5, -3)
- Or go up 1, left 5 → (-5, -1)
Plot (0, -2), (5, -3), and draw line.
✔ Graph matches — it’s a shallow downward sloping line crossing y-axis at -2.
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Problem 2: y = -5x – 1
- Y-intercept: (0, -1)
- Slope = -5 → down 5, right 1 → from (0,-1) to (1, -6)
- Or up 5, left 1 → (-1, 4)
Plot (0, -1) and (1, -6). Draw steep downward line.
✔ Graph matches — very steep negative slope, crosses y-axis at -1.
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Problem 3: y = -⁵/₂x
This is same as y = -²·⁵x + 0 → so y-intercept is 0 → passes through origin (0,0)
Slope = -5/2 → down 5, right 2 → from (0,0) to (2, -5)
Or up 5, left 2 → (-2, 5)
Plot (0,0) and (2, -5). Draw steep downward line through origin.
✔ Graph matches — goes through origin, steep negative slope.
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Problem 4: y = -7x + 3
- Y-intercept: (0, 3)
- Slope = -7 → down 7, right 1 → (1, -4)
- Or up 7, left 1 → (-1, 10) — but that’s off grid, so use (1, -4)
Plot (0,3) and (1, -4). Very steep downward line.
✔ Graph matches — starts high on y-axis, drops sharply.
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Problem 5: y = 2x – 5
- Y-intercept: (0, -5)
- Slope = 2 → up 2, right 1 → (1, -3); then (2, -1); (3, 1) etc.
Plot (0, -5) and (1, -3). Upward sloping line.
✔ Graph matches — crosses y-axis at -5, rises steadily.
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Problem 6: y = -6x + 1
- Y-intercept: (0, 1)
- Slope = -6 → down 6, right 1 → (1, -5)
- Or up 6, left 1 → (-1, 7) — maybe too high, so use (1, -5)
Plot (0,1) and (1, -5). Steep downward line.
✔ Graph matches — starts at y=1, drops fast.
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All graphs are correctly sketched based on their equations. Each line has the correct y-intercept and slope direction/magnitude.
Final Answer: All six graphs are correctly drawn according to their equations.
Parent Tip: Review the logic above to help your child master the concept of graphing linear equations worksheet kuta.
