Answer :
Alright class, let's go through the steps to convert the given equation from Standard Form to Slope-Intercept Form. Our task is to convert [tex]\(8x + 2y = 16\)[/tex] to the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
### Step-by-Step Solution:
1. Start with the given Standard Form equation:
[tex]\[ 8x + 2y = 16 \][/tex]
2. Isolate the [tex]\(y\)[/tex]-term on one side of the equation:
To do this, we first need to get rid of [tex]\(8x\)[/tex] from the left side. We can do this by subtracting [tex]\(8x\)[/tex] from both sides:
[tex]\[ 2y = -8x + 16 \][/tex]
3. Solve for [tex]\(y\)[/tex]:
To convert the equation to the slope-intercept form [tex]\(y = mx + b\)[/tex], we need to get [tex]\(y\)[/tex] by itself. This involves dividing every term by 2:
[tex]\[ y = \frac{-8}{2}x + \frac{16}{2} \][/tex]
4. Simplify the fractions:
[tex]\[ y = -4x + 8 \][/tex]
Now, the equation is in slope-intercept form [tex]\(y = mx + b\)[/tex].
### Identify the Slope and Y-Intercept:
- Slope ([tex]\(m\)[/tex]): This is the coefficient of [tex]\(x\)[/tex]. From the equation [tex]\(y = -4x + 8\)[/tex], the slope [tex]\(m\)[/tex] is:
[tex]\[ m = -4 \][/tex]
- Y-Intercept ([tex]\(b\)[/tex]): This is the constant term. From the equation [tex]\(y = -4x + 8\)[/tex], the y-intercept [tex]\(b\)[/tex] is:
[tex]\[ b = 8 \][/tex]
### Final Answers:
- The slope is [tex]\(-4\)[/tex].
- The y-intercept is [tex]\(8\)[/tex].
Well done! You've now successfully converted the equation from Standard Form to Slope-Intercept Form and identified the slope and y-intercept.
### Step-by-Step Solution:
1. Start with the given Standard Form equation:
[tex]\[ 8x + 2y = 16 \][/tex]
2. Isolate the [tex]\(y\)[/tex]-term on one side of the equation:
To do this, we first need to get rid of [tex]\(8x\)[/tex] from the left side. We can do this by subtracting [tex]\(8x\)[/tex] from both sides:
[tex]\[ 2y = -8x + 16 \][/tex]
3. Solve for [tex]\(y\)[/tex]:
To convert the equation to the slope-intercept form [tex]\(y = mx + b\)[/tex], we need to get [tex]\(y\)[/tex] by itself. This involves dividing every term by 2:
[tex]\[ y = \frac{-8}{2}x + \frac{16}{2} \][/tex]
4. Simplify the fractions:
[tex]\[ y = -4x + 8 \][/tex]
Now, the equation is in slope-intercept form [tex]\(y = mx + b\)[/tex].
### Identify the Slope and Y-Intercept:
- Slope ([tex]\(m\)[/tex]): This is the coefficient of [tex]\(x\)[/tex]. From the equation [tex]\(y = -4x + 8\)[/tex], the slope [tex]\(m\)[/tex] is:
[tex]\[ m = -4 \][/tex]
- Y-Intercept ([tex]\(b\)[/tex]): This is the constant term. From the equation [tex]\(y = -4x + 8\)[/tex], the y-intercept [tex]\(b\)[/tex] is:
[tex]\[ b = 8 \][/tex]
### Final Answers:
- The slope is [tex]\(-4\)[/tex].
- The y-intercept is [tex]\(8\)[/tex].
Well done! You've now successfully converted the equation from Standard Form to Slope-Intercept Form and identified the slope and y-intercept.
