The task involves graphing equations in
point-slope form and identifying the slope (\( m \)) and a point on the line for each equation. The point-slope form of a linear equation is given by:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is a point on the line.
Step-by-Step Solution:
#### 1. Equation: \( y - 1 = -(x - 5) \)
-
Slope (\( m \)): The coefficient of \( (x - 5) \) is \(-1\). So, \( m = -1 \).
-
Point (\( x_1, y_1 \)): From the equation \( y - 1 = -(x - 5) \), we see that \( x_1 = 5 \) and \( y_1 = 1 \). So, the point is \( (5, 1) \).
#### 2. Equation: \( y + 2 = 3(x + 1) \)
-
Slope (\( m \)): The coefficient of \( (x + 1) \) is \( 3 \). So, \( m = 3 \).
-
Point (\( x_1, y_1 \)): From the equation \( y + 2 = 3(x + 1) \), we see that \( x_1 = -1 \) and \( y_1 = -2 \). So, the point is \( (-1, -2) \).
#### 3. Equation: \( y - 4 = 2(x + 2) \)
-
Slope (\( m \)): The coefficient of \( (x + 2) \) is \( 2 \). So, \( m = 2 \).
-
Point (\( x_1, y_1 \)): From the equation \( y - 4 = 2(x + 2) \), we see that \( x_1 = -2 \) and \( y_1 = 4 \). So, the point is \( (-2, 4) \).
#### 4. Equation: \( y + 3 = 2(x - 4) \)
-
Slope (\( m \)): The coefficient of \( (x - 4) \) is \( 2 \). So, \( m = 2 \).
-
Point (\( x_1, y_1 \)): From the equation \( y + 3 = 2(x - 4) \), we see that \( x_1 = 4 \) and \( y_1 = -3 \). So, the point is \( (4, -3) \).
Summary of Results:
1. \( y - 1 = -(x - 5) \)
- \( m = -1 \)
- Point: \( (5, 1) \)
2. \( y + 2 = 3(x + 1) \)
- \( m = 3 \)
- Point: \( (-1, -2) \)
3. \( y - 4 = 2(x + 2) \)
- \( m = 2 \)
- Point: \( (-2, 4) \)
4. \( y + 3 = 2(x - 4) \)
- \( m = 2 \)
- Point: \( (4, -3) \)
Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & m = -1, \text{ Point} = (5, 1) \\
2. & m = 3, \text{ Point} = (-1, -2) \\
3. & m = 2, \text{ Point} = (-2, 4) \\
4. & m = 2, \text{ Point} = (4, -3) \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of point slope form worksheet.
