Algebra - "Solve for x" Challenge¶
Problem Statement¶
Determine the equation of a straight line that has a y-intercept of 1, and which is perpendicular to the line that is represetned by the equation below:
Step-by-Step Solution¶
To determine the equation of a straight line that has a y-intercept of 1 and is perpendicular to the line represented by the equation \( y = 2x + 3 \), follow these steps:
Step 1: Determine the slope of the perpendicular line¶
The given line is \( y = 2x + 3 \). In this slope-intercept form, \( y = mx + b \), the slope \( m \) is 2.
For a line perpendicular to this one, the slope will be the negative reciprocal of 2.
Step 2: Use the slope-intercept form to write the new line's equation¶
The general form of the equation of a line is:
where \( m \) is the slope and \( b \) is the y-intercept.
Given: - The slope of the perpendicular line is \( -\frac{1}{2} \). - The y-intercept is 1.
Substitute these values into the slope-intercept form:
Step 3: Write the final equation¶
The equation of the straight line that is perpendicular to \( y = 2x + 3 \) and has a y-intercept of 1 is:
Solution:¶
- Slope of the given line: 2
- Slope of the perpendicular line: \(-\frac{1}{2}\)
- Y-intercept of the perpendicular line: 1
Thus, the equation of the desired line is: