Find the equation of the line that is perpendicular to y = 5x + 2 and passes thr

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Question: Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.

Options:

Correct Answer: y = -5x

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.

Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.

Find the equation of the line that is perpendicular to y = 5x + 2 and passes through the origin.

Correct Answer: y = -1/5x

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.

Slope of a Line – Understanding that the slope of a line in the form y = mx + b is represented by 'm'.
Perpendicular Lines – Knowing that the slopes of two perpendicular lines are negative reciprocals of each other.
Equation of a Line – Using the slope-intercept form y = mx + c to write the equation of a line.
Point-Slope Form – Recognizing that a line passing through the origin has a y-intercept (c) of 0.