Question

Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses

y=12x−3
y
=
1
2
x
−
3
y equals Start Fraction 1 over 2 End Fraction x minus 3

−8y=−4x+24
−
8
y
=
−
4
x
+
24
negative 8 y equals negative 4 x plus 24

4x−8y−24=0
4
x
−
8
y
−
24
=
0
4 x minus 8 y minus 24 equals 0

4x−8y=24

Answer 1

To transform the linear equation \(4x - 8y = 24\) into slope-intercept form, which is \(y = mx + b\), follow these steps:

1. Start with the equation:
\[
4x - 8y = 24
\]

2. Isolate the term with \(y\) by subtracting \(4x\) from both sides:
\[
-8y = -4x + 24
\]

3. Divide all terms by \(-8\) to solve for \(y\):
\[
y = \frac{-4x}{-8} + \frac{24}{-8}
\]

4. Simplifying the fractions gives:
\[
y = \frac{1}{2}x - 3
\]

Thus, the equation in slope-intercept form is:
\[
y = \frac{1}{2}x - 3
\]

So the correct response is:
\( y = \frac{1}{2}x - 3 \) (y equals Start Fraction 1 over 2 End Fraction x minus 3).

Answer 2

Write y−2=32(x+2)
y
−
2
=
3
2
(
x
+
2
)
in slope-intercept form.(1 point)
Responses

y=32+5x
y
=
3
2
+
5
x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y=32x+6
y
=
3
2
x
+
6
y equals Start Fraction 3 over 2 End Fraction x plus 6

y=32x+5
y
=
3
2
x
+
5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=32x+32

Answer 3

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form \( y = mx + b \), follow these steps:

1. Start with the equation:
\[
y - 2 = \frac{3}{2}(x + 2)
\]

2. Distribute \(\frac{3}{2}\) on the right side:
\[
y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2
\]
\[
y - 2 = \frac{3}{2}x + 3
\]

3. Add 2 to both sides to solve for \(y\):
\[
y = \frac{3}{2}x + 3 + 2
\]
\[
y = \frac{3}{2}x + 5
\]

Thus, the equation in slope-intercept form is:
\[
y = \frac{3}{2}x + 5
\]

So the correct response is:
\( y = \frac{3}{2}x + 5 \) (y equals Start Fraction 3 over 2 End Fraction x plus 5).