Question

An expression is shown/

4(34x+3x−2)−2(3x2+1+3x)

Rewrite an equivalent expression with the fewest terms possible

(3 points)
Answer
An equation is shown.

y−5 = −3(x+6)
(2 points)
The equation rewritten in slope-intercept form is
.

The point
is on the graph of the line.
Answer
What is the slope-intercept form of the linear equation 5x+3y=9
?(1 point)
Responses

y = −53x+3
y = −53x+3

y = 53x+3
y = 53x+3

y = −53x+9
y = −53x+9

y = −5x+3
y = −5x+3

y = 53x−3
Answered by GPT-4o mini
To simplify the expression \( 4(34x + 3x - 2) - 2(3x^2 + 1 + 3x) \), we'll follow the steps of distributing and combining like terms.

1. Distribute the \(4\) and \(-2\):

\[
4(34x) + 4(3x) + 4(-2) - 2(3x^2) - 2(1) - 2(3x)
\]

Simplifying that gives us:

\[
136x + 12x - 8 - 6x^2 - 2 - 6x
\]

2. Now, combine like terms:

- Combine the \(x\) terms:
\[
136x + 12x - 6x = 142x
\]

- The constant terms:
\[
-8 - 2 = -10
\]

Putting it all together, we have:

\[
-6x^2 + 142x - 10
\]

So the final simplified expression is:

\[
-6x^2 + 142x - 10
\]

This is the equivalent expression with the fewest terms possible.
Answered by GPT-4o mini
To rewrite the equation \( y - 5 = -3(x + 6) \) in slope-intercept form (which is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

1. **Distribute the \(-3\)** on the right-hand side:

\[
y - 5 = -3x - 18
\]

2. **Add \(5\)** to both sides to isolate \(y\):

\[
y = -3x - 18 + 5
\]

\[
y = -3x - 13
\]

So, the equation rewritten in slope-intercept form is:

\[
y = -3x - 13
\]

Next, to determine a point that is on the graph of the line, we can choose any \(x\) value and substitute it into the equation to find the corresponding \(y\) value.

Let's choose \(x = 0\):

\[
y = -3(0) - 13 = -13
\]

Thus, the point \((0, -13)\) is on the graph of the line.

### Final Results:
- The equation in slope-intercept form is: **\(y = -3x - 13\)**
- A point on the graph of the line is: **\((0, -13)\)**
Answered by GPT-4o mini
To convert the equation \(5x + 3y = 9\) to slope-intercept form \(y = mx + b\), we need to isolate \(y\).

Here are the steps:

1. **Subtract \(5x\) from both sides**:
\[
3y = -5x + 9
\]

2. **Divide every term by \(3\)** to solve for \(y\):
\[
y = -\frac{5}{3}x + 3
\]

So the slope-intercept form of the equation is:

\[
y = -\frac{5}{3}x + 3
\]

From the given options, the correct response is:

**y = −\(\frac{5}{3}\)x + 3**.