Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.
Practice Questions
1 question
Q1
Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.
y = -1/5x
y = 5x
y = -5x
y = 1/5x
The slope of the given line is 5. The slope of the perpendicular line is -1/5. Using y = mx + c, we get y = -1/5x.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.
Solution: The slope of the given line is 5. The slope of the perpendicular line is -1/5. Using y = mx + c, we get y = -1/5x.
Steps: 4
Step 1: Identify the slope of the given line. The equation is y = 5x + 2, so the slope (m) is 5.
Step 2: Find the slope of the line that is perpendicular to the given line. The slope of a perpendicular line is the negative reciprocal of the original slope. So, the negative reciprocal of 5 is -1/5.
Step 3: Use the slope-intercept form of a line, which is y = mx + c. Here, m is the slope we found (-1/5) and c is the y-intercept. Since the line passes through the origin, c = 0.
Step 4: Substitute the slope and y-intercept into the equation. This gives us y = -1/5x + 0, which simplifies to y = -1/5x.
