To write the equation of a line in slope-intercept form, we use the formula:
$$y = mx + b$$
where:
* $m$ is the
slope (rise over run).
* $b$ is the
y-intercept (where the line crosses the vertical y-axis).
Here is the step-by-step solution for each problem:
1. Graph 1
*
Find the y-intercept ($b$): The line crosses the y-axis at positive 2. So, $b = 2$.
*
Find the slope ($m$): Start at the y-intercept $(0, 2)$. To get to the next clear point on the grid, which is $(-3, 1)$, we go
down 1 unit and
left 3 units.
* Rise = $-1$, Run = $-3$.
* Slope $m = \frac{-1}{-3} = \frac{1}{3}$.
*
Equation: $y = \frac{1}{3}x + 2$
2. Graph 2
*
Find the y-intercept ($b$): The line crosses the y-axis at 0. So, $b = 0$.
*
Find the slope ($m$): Start at $(0, 0)$. To get to the next point $(3, -1)$, we go
down 1 unit and
right 3 units.
* Rise = $-1$, Run = $3$.
* Slope $m = -\frac{1}{3}$.
*
Equation: $y = -\frac{1}{3}x$
3. Graph 3
*
Find the y-intercept ($b$): The line crosses the y-axis at 0. So, $b = 0$.
*
Find the slope ($m$): Start at $(0, 0)$. To get to the point $(2, -2)$, we go
down 2 units and
right 2 units.
* Rise = $-2$, Run = $2$.
* Slope $m = \frac{-2}{2} = -1$.
*
Equation: $y = -x$
4. Graph 4
*
Find the y-intercept ($b$): The line crosses the y-axis at negative 3. So, $b = -3$.
*
Find the slope ($m$): Start at $(0, -3)$. To get to the point $(1, -1)$, we go
up 2 units and
right 1 unit.
* Rise = $2$, Run = $1$.
* Slope $m = \frac{2}{1} = 2$.
*
Equation: $y = 2x - 3$
5. Graph 5
*
Find the y-intercept ($b$): The line crosses the y-axis at 0. So, $b = 0$.
*
Find the slope ($m$): Start at $(0, 0)$. To get to the point $(1, -1)$, we go
down 1 unit and
right 1 unit.
* Rise = $-1$, Run = $1$.
* Slope $m = -1$.
*
Equation: $y = -x$
6. Graph 6
*
Find the y-intercept ($b$): The line crosses the y-axis at 1. So, $b = 1$.
*
Find the slope ($m$): Start at $(0, 1)$. To get to the point $(4, 3)$, we go
up 2 units and
right 4 units.
* Rise = $2$, Run = $4$.
* Slope $m = \frac{2}{4}$, which simplifies to $\frac{1}{2}$.
*
Equation: $y = \frac{1}{2}x + 1$
Final Answer:
1. Equation: $y = \frac{1}{3}x + 2$
2. Equation: $y = -\frac{1}{3}x$
3. Equation: $y = -x$
4. Equation: $y = 2x - 3$
5. Equation: $y = -x$
6. Equation: $y = \frac{1}{2}x + 1$
Parent Tip: Review the logic above to help your child master the concept of writing in slope intercept form worksheet.
