Find the slope-intercept form of the equation of the line that passes through the point (5, -3) and 
perpendicular to line y = 2x + 1 

The slope-intercept form of a line is written as:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Identify the slope of the given line
The given line is \( y = 2x + 1 \). The slope of this line is the coefficient of \( x \), which is \( 2 \).

### Step 2: Find the slope of the perpendicular line
Lines that are perpendicular to each other have slopes that are negative reciprocals. If the slope of the given line is \( 2 \), the slope of the perpendicular line will be:

\[
m_{\text{perpendicular}} = -\frac{1}{2}
\]

### Step 3: Use the point-slope form
The line passes through the point \( (5, -3) \), so we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Substitute \( m = -\frac{1}{2} \), \( x_1 = 5 \), and \( y_1 = -3 \):

\[
y - (-3) = -\frac{1}{2}(x - 5)
\]

Simplify the equation:

\[
y + 3 = -\frac{1}{2}(x - 5)
\]

### Step 4: Simplify to slope-intercept form
Distribute the \( -\frac{1}{2} \) on the right-hand side:

\[
y + 3 = -\frac{1}{2}x + \frac{5}{2}
\]

Subtract 3 from both sides to solve for \( y \):

\[
y = -\frac{1}{2}x + \frac{5}{2} - 3
\]

Convert 3 to a fraction with a denominator of 2:

\[
y = -\frac{1}{2}x + \frac{5}{2} - \frac{6}{2}
\]

Simplify:

\[
y = -\frac{1}{2}x - \frac{1}{2}
\]

### Final Equation
The slope-intercept form of the equation of the line is:

\[
y = -\frac{1}{2}x - \frac{1}{2}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the slope-intercept form of a line parallel to \( y = 3x - 2 \)?
2. How do you find the equation of a line given two points?
3. What is the relationship between the slopes of parallel and perpendicular lines?
4. How do you convert from point-slope form to slope-intercept form?
5. What is the standard form of a line, and how does it relate to slope-intercept form?

**Tip**: Perpendicular lines always have slopes that are negative reciprocals, which means their product is \( -1 \).

Find the slope-intercept form of the equation of the line that passes through the point (5, -3) and perpendicular to line y = 2x + 1.

Learn how to find the slope-intercept form of a line that passes through the point (5, -3) and is perpendicular to the line y = 2x + 1. This solution involves key concepts in linear equations, including slope, perpendicularity, and point-slope form. Suitable for students in Grades 9-10.

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