To match each graph to its equation, we need to look at two things for every line:
1.
The y-intercept ($b$): This is where the line crosses the vertical y-axis.
2.
The slope ($m$): This tells us how steep the line is and which way it goes. We can find this by counting "rise over run" from one grid intersection to another.
Let's analyze each graph one by step.
Graph 1:
*
y-intercept: The line crosses the y-axis at $+3$. So, $b = 3$.
*
Slope: Starting from $(0, 3)$, if we go right 2 units, we go down 1 unit to hit the next grid intersection at $(2, 2)$.
* Rise = $-1$, Run = $2$.
* Slope $m = -1/2$.
*
Equation: $y = -1/2x + 3$.
*
Match: This matches option
B.
Graph 2:
*
y-intercept: The line crosses the y-axis at $-2$. So, $b = -2$.
*
Slope: Starting from $(0, -2)$, if we go right 3 units, we go up 1 unit to hit $(3, -1)$.
* Rise = $1$, Run = $3$.
* Slope $m = 1/3$.
*
Equation: $y = 1/3x - 2$.
*
Match: This matches option
A.
Graph 3:
*
y-intercept: The line crosses the y-axis at $+5$. So, $b = 5$.
*
Slope: Starting from $(0, 5)$, if we go right 1 unit, we go down 2 units to hit $(1, 3)$.
* Rise = $-2$, Run = $1$.
* Slope $m = -2$.
*
Equation: $y = -2x + 5$.
*
Match: This matches option
E.
Graph 4:
*
y-intercept: The line crosses the y-axis at $+1$. So, $b = 1$.
*
Slope: Starting from $(0, 1)$, if we go right 1 unit, we go down 4 units to hit $(1, -3)$.
* Rise = $-4$, Run = $1$.
* Slope $m = -4$.
*
Equation: $y = -4x + 1$.
*
Match: This matches option
F.
Graph 5:
*
y-intercept: The line crosses the y-axis at $-3$. So, $b = -3$.
*
Slope: Starting from $(0, -3)$, if we go right 1 unit, we go up 3 units to hit $(1, 0)$.
* Rise = $3$, Run = $1$.
* Slope $m = 3$.
*
Equation: $y = 3x - 3$.
*
Match: This matches option
G.
Graph 6:
*
y-intercept: The line crosses the y-axis at $+2$. So, $b = 2$.
*
Slope: Starting from $(0, 2)$, if we go right 3 units, we go up 2 units to hit $(3, 4)$.
* Rise = $2$, Run = $3$.
* Slope $m = 2/3$.
*
Equation: $y = 2/3x + 2$.
*
Match: This matches option
H.
*(Note: Options C and D were not used in this set.)*
Final Answer:
1-B, 2-A, 3-E, 4-F, 5-G, 6-H
Parent Tip: Review the logic above to help your child master the concept of matching equations and graphs worksheet.
