Let’s solve each problem step by step. We’re looking for the
slope-intercept form of each line, which is:
>
y = mx + b
Where:
-
m is the slope (how steep the line is)
-
b is the y-intercept (where the line crosses the y-axis)
---
Problem 1)
Look at the graph. The line goes through two easy points:
→ Let’s pick
(0, 4) — that’s where it crosses the y-axis → so
b = 4
→ Another point:
(2, 0)
Now find the slope
m:
> Slope = rise / run = (change in y) / (change in x)
From (0, 4) to (2, 0):
Change in y = 0 - 4 =
-4
Change in x = 2 - 0 =
2
So slope m = -4 / 2 =
-2
Equation:
y = -2x + 4
✔ Check: Plug in x=0 → y=4 ✔️
Plug in x=2 → y=-4+4=0 ✔️
---
Problem 2)
Line crosses y-axis at
(0, -2) → so
b = -2
Another point: let’s use
(2, -6)
Slope from (0, -2) to (2, -6):
Change in y = -6 - (-2) = -4
Change in x = 2 - 0 = 2
Slope m = -4 / 2 =
-2
Equation:
y = -2x - 2
✔ Check: x=0 → y=-2 ✔️
x=2 → y=-4-2=-6 ✔️
---
Problem 3)
Line crosses y-axis at
(0, 5)? Wait — look again.
Actually, when x=0, y=5? No — let’s check carefully.
Looking at the grid:
At x=0, the line is at y=5? Actually, no — let’s pick two clear points.
Better points:
→ When x = -1, y = 2
→ When x = 0, y = 5? Wait — actually, looking again...
Wait — let’s count squares.
From left to right:
When x = -2, y = -1
When x = 0, y = 5? That seems too steep.
Wait — better:
Pick (0, 5) and (1, 8)? But that might not be on the line.
Actually, let’s go with:
Point A: (-1, 2)
Point B: (0, 5)
Then slope = (5 - 2)/(0 - (-1)) = 3/1 =
3
Y-intercept: when x=0, y=5 →
b=5
Equation:
y = 3x + 5
✔ Check: x=-1 → y=3(-1)+5=2 ✔️
x=0 → y=5 ✔️
But wait — does the line really pass through (0,5)? Looking at the graph again...
Actually, in problem 3, the line passes through:
→ (0, 5) — yes, top of y-axis
→ And (-1, 2) — yes, one left, three down → slope = 3
Yes, correct.
---
Problem 4)
Line crosses y-axis at
(0, 3) → so
b = 3
Another point: let’s take
(1, 5)
Slope = (5 - 3)/(1 - 0) = 2/1 =
2
Equation:
y = 2x + 3
✔ Check: x=0 → y=3 ✔️
x=1 → y=2+3=5 ✔️
Also check another point: x=-1 → y=2(-1)+3=1 → does the line go through (-1,1)? Yes, looks like it.
Perfect.
---
Final Answer:
1) y = -2x + 4
2) y = -2x - 2
3) y = 3x + 5
4) y = 2x + 3
Parent Tip: Review the logic above to help your child master the concept of solving equations worksheet kuta.
