To graph a line in slope-intercept form ($y = mx + b$), you need two things:
1.
The y-intercept ($b$): This is where the line crosses the vertical y-axis. Start your point here.
2.
The slope ($m$): This tells you how to move from that first point to find the next one. It is written as $\frac{\text{rise}}{\text{run}}$ (change in $y$ over change in $x$).
Here is the step-by-step solution for each problem on the worksheet:
1) $y = 2x + 8$
*
Start: The y-intercept is $+8$. Put a dot at $(0, 8)$ on the y-axis.
*
Move: The slope is $2$, which means $\frac{2}{1}$. From your starting dot, go
up 2 units and
right 1 unit. Put a second dot there.
*
Draw: Connect the dots with a straight line.
2) $y = 4$
*
Start: This equation has no $x$, which means the slope is $0$. The y-intercept is $4$.
*
Draw: Since the slope is zero, the line is perfectly horizontal. Draw a straight line across the graph at height $4$ (passing through $y=4$).
3) $y = -x + 4$
*
Start: The y-intercept is $+4$. Put a dot at $(0, 4)$.
*
Move: The slope is $-1$ (implied by $-x$), which is $\frac{-1}{1}$. From your starting dot, go
down 1 unit and
right 1 unit. Put a second dot there.
*
Draw: Connect the dots with a straight line.
4) $y = -4x + 3$
*
Start: The y-intercept is $+3$. Put a dot at $(0, 3)$.
*
Move: The slope is $-4$, which is $\frac{-4}{1}$. From your starting dot, go
down 4 units and
right 1 unit. Put a second dot there.
*
Draw: Connect the dots with a straight line.
5) $y = -3$
*
Start: Like problem #2, this has no $x$, so the slope is $0$. The y-intercept is $-3$.
*
Draw: Draw a straight horizontal line across the graph at height $-3$ (below the x-axis).
6) $y = -x$
*
Start: There is no number added at the end, so the y-intercept is $0$. Start at the origin $(0,0)$, where the axes cross.
*
Move: The slope is $-1$ ($\frac{-1}{1}$). From the center, go
down 1 unit and
right 1 unit. Put a dot there.
*
Draw: Connect the center point and your new dot with a straight line.
Final Answer:
See the descriptions above for how to draw each line:
1. Line starts at $(0,8)$ and goes up steeply.
2. Horizontal line at $y=4$.
3. Line starts at $(0,4)$ and goes down gently.
4. Line starts at $(0,3)$ and goes down very steeply.
5. Horizontal line at $y=-3$.
6. Line goes through the center $(0,0)$ and goes down gently.
Parent Tip: Review the logic above to help your child master the concept of slope from a graph worksheet.
