Let’s solve each problem one by one. We’re looking for the
slope-intercept form of a line, which is:
>
y = mx + b
Where:
-
m = slope (rise over run)
-
b = y-intercept (where the line crosses the y-axis)
We’ll find two points on each line, calculate the slope, and then plug in to get the equation.
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Problem 1)
Line goes through (0, -3) and (1, 2).
Slope m = (2 - (-3)) / (1 - 0) = 5/1 = 5
Y-intercept b = -3 (since it crosses at x=0, y=-3)
→ Equation:
y = 5x - 3
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Problem 2)
Line goes through (0, 2) and (4, 0).
Slope m = (0 - 2)/(4 - 0) = -2/4 = -1/2
Y-intercept b = 2
→ Equation:
y = -½x + 2
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Problem 3)
Line goes through (0, -3) and (4, -6).
Slope m = (-6 - (-3))/(4 - 0) = (-3)/4 = -¾
Y-intercept b = -3
→ Equation:
y = -¾x - 3
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Problem 4)
Horizontal line at y = 3 → slope = 0
Equation:
y = 3
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Problem 5)
Line goes through (0, 3) and (-4, 0).
Slope m = (0 - 3)/(-4 - 0) = (-3)/(-4) = ¾
Y-intercept b = 3
→ Equation:
y = ¾x + 3
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Problem 6)
Line goes through (0, -3) and (1, 2).
Slope m = (2 - (-3))/(1 - 0) = 5/1 = 5
Y-intercept b = -3
→ Equation:
y = 5x - 3
*(Same as #1 — different graph but same line? Let me double-check... Actually, looking again: this line passes through (0,-3) and (1,2), yes — so same as #1. But maybe it's intentional.)*
Wait — let me check coordinates again from grid.
Actually, in #6, when x=0, y=-3; when x=1, y=2 → same as #1. So yes, same equation.
But let’s confirm with another point: if x=2, y should be 7? On the graph, does it go up that fast? Yes — steep positive slope.
So still:
y = 5x - 3
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Problem 7)
Line goes through (0, 3) and (-1, -1).
Slope m = (-1 - 3)/(-1 - 0) = (-4)/(-1) = 4
Y-intercept b = 3
→ Equation:
y = 4x + 3
Check: At x = -1, y = 4*(-1)+3 = -1 → matches.
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Problem 8)
Line goes through (0, 3) and (-2, -1).
Slope m = (-1 - 3)/(-2 - 0) = (-4)/(-2) = 2
Y-intercept b = 3
→ Equation:
y = 2x + 3
Check: At x = -2, y = 2*(-2)+3 = -4+3 = -1 → correct.
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Now let’s list all answers clearly.
Final Answer:
1) y = 5x - 3
2) y = -½x + 2
3) y = -¾x - 3
4) y = 3
5) y = ¾x + 3
6) y = 5x - 3
7) y = 4x + 3
8) y = 2x + 3
Parent Tip: Review the logic above to help your child master the concept of writing equations from a graph worksheet.
![Write An Equation From A Graph Worksheets [PDF] (7.G.B.4): 8th ...](/images2/writing-equations-from-a-graph-worksheet/writing-equations-from-a-graph-worksheet-20.png)
