Let’s solve each graph one by one to find the equation of the line.
We’ll use the 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)
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Graph 1 (Top Left — Blue Line)
Step 1: Find the y-intercept (b).
The line crosses the y-axis at
y = 3 → so
b = 3
Step 2: Find the slope (m).
Pick two points on the line. Let’s use (0, 3) and (-1, -1).
From (0,3) to (-1,-1):
→ Down 4 units (rise = -4), left 1 unit (run = -1)
Slope m = rise/run = (-4)/(-1) =
4
Check with another point: from (0,3) to (1,7)? Wait — looking at the graph, when x=1, y=7? Actually, let’s check carefully.
Wait — actually, from (0,3) to (-1, -1): that’s correct. But let’s verify with grid.
Actually, looking again: from (0,3) to (-1, -1) — yes, down 4, left 1 → slope = 4.
But wait — if x increases by 1, how much does y increase? From x=-1 to x=0, y goes from -1 to 3 → that’s +4 in y for +1 in x → slope = 4.
So equation:
y = 4x + 3
✔ Double-check: When x = -1, y = 4*(-1)+3 = -1 → matches graph. Good.
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Graph 2 (Top Right — Red Line)
Step 1: Y-intercept (b)
Line crosses y-axis at
y = 6 → b = 6
Step 2: Slope (m)
Pick two points: (0,6) and (3,3)
From (0,6) to (3,3): down 3, right 3 → slope = -3/3 =
-1
Equation:
y = -x + 6
✔ Check: When x=6, y = -6+6=0 → looks like it passes through (6,0) on graph. Correct.
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Graph 3 (Bottom Left — Green Line)
Step 1: Y-intercept (b)
Line crosses y-axis at
y = -5 → b = -5
Step 2: Slope (m)
Pick two points: (0, -5) and (5, 0)
From (0,-5) to (5,0): up 5, right 5 → slope = 5/5 =
1
Equation:
y = x - 5
✔ Check: When x=10, y=5 → should be on line? Looking at graph, yes — green line goes through (10,5). Correct.
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Graph 4 (Bottom Right — Purple Line)
Step 1: Y-intercept (b)
Line crosses y-axis at
y = -3 → b = -3
Step 2: Slope (m)
Pick two points: (0, -3) and (3, -9)
From (0,-3) to (3,-9): down 6, right 3 → slope = -6/3 =
-2
Equation:
y = -2x - 3
✔ Check: When x = -3, y = -2*(-3) -3 = 6 - 3 = 3 → does the line pass through (-3,3)? Looking at graph, yes — purple line goes through there. Correct.
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Final Answer:
Graph 1 (Blue): y = 4x + 3
Graph 2 (Red): y = -x + 6
Graph 3 (Green): y = x - 5
Graph 4 (Purple): y = -2x - 3
Parent Tip: Review the logic above to help your child master the concept of linear functions worksheet algebra 1.
