Question

The following 3 equations are in point-slope form. What points must each equation pass through?
c. y - 3 = 5(x + 2)
*
1 point
(0, 0)
(2, 3)
(3, -2)
(-2, 3)
Convert 3x + 3y = 9 to slope intercept point.
*
1 point
y = -3x + 9
y = -x + 9
y = -x + 3
y = x + 3

Answer 1

gimmie the answer number them

Answer 2

Let's analyze each part of your question one at a time.

### Part 1: Finding the point for the equation \( y - 3 = 5(x + 2) \)

The equation is in point-slope form, which can be compared to \( y - y_1 = m(x - x_1) \).

Here, the equation \( y - 3 = 5(x + 2) \) can be rewritten as:
1. Identifying \( y_1 = 3 \) and \( m = 5 \).
2. The point it passes through is found by taking \( x_1 = -2 \).

So, it passes through the point \((-2, 3)\).

From the options given:
- (0, 0)
- (2, 3)
- (3, -2)
- **(-2, 3)** (This is the correct answer.)

### Part 2: Converting \( 3x + 3y = 9 \) to slope-intercept form

To convert the given equation to slope-intercept form \( y = mx + b \):

1. Start from \( 3x + 3y = 9 \).
2. Subtract \( 3x \) from both sides:
\[
3y = -3x + 9
\]
3. Divide every term by \( 3 \):
\[
y = -x + 3
\]

So the equation in slope-intercept form is \( y = -x + 3 \).

From the options given:
- \( y = -3x + 9 \)
- \( y = -x + 9 \)
- **\( y = -x + 3 \)** (This is the correct answer.)
- \( y = x + 3 \)

### Summary of Answers
1. The equation \( y - 3 = 5(x + 2) \) must pass through the point **(-2, 3)**.
2. The conversion of \( 3x + 3y = 9 \) is \( y = -x + 3 \).

Answer 3

Certainly! Here are the answers numbered:

1. **(-2, 3)**
2. **\( y = -x + 3 \)**