To find the slope and a point on the line given by the equation \( y + 2 = 3(x - 7) \), we need to follow these steps:
1. Convert the equation to slope-intercept form ( \(y = mx + b\) ):
- Start with the given equation: \( y + 2 = 3(x - 7) \)
- Expand the right-hand side: \( y + 2 = 3x - 21 \)
- Subtract 2 from both sides to solve for \( y \): \( y = 3x - 21 - 2 \)
- Simplify the right-hand side: \( y = 3x - 23 \)
2. In the slope-intercept form \( y = mx + b \), the coefficient of \( x \) (which is 3) represents the slope \( m \). Therefore, the slope of the line is \( 3 \).
3. Find a point on the line:
- To find a specific point on the line, we can use the original equation. For simplicity, we can find the point where \( x = 7 \):
- Substitute \( x = 7 \) into the original equation: \( y + 2 = 3(7 - 7) \)
- Simplify the expression inside the parentheses: \( y + 2 = 3 \times 0 \)
- This reduces to \( y + 2 = 0 \)
- Solve for \( y \): \( y = -2 \)
So, the point \((7, -2)\) lies on the line.
Given the steps, the correct answer is:
C. The slope is 3 and [tex]\( (7, -2) \)[/tex] is on the line.
