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Parallel & Perpendicular Lines Practice

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Question
Find the equation of the line that is parallel to the line y=25x+1
and passes through the point (5,5)
.(1 point)
The line that is parallel to y=25x+1
and passes through the point (5,5)
is y=25x+
.
Remaining Attempts : 2

3 answers

To find the equation of the line that is parallel to the line \( y = 25x + 1 \) and passes through the point \( (5, 5) \), we need to know that parallel lines have the same slope.

The slope of the given line \( y = 25x + 1 \) is \( 25 \). Therefore, the slope of the line we want to find will also be \( 25 \).

We can use the point-slope form of a linear equation, which is given by: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through.

Substituting \( m = 25 \) and the point \( (5, 5) \): \[ y - 5 = 25(x - 5) \]

Now we can simplify this: \[ y - 5 = 25x - 125 \] \[ y = 25x - 120 \]

Thus, the equation of the line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5, 5) \) is: \[ y = 25x - 120 \]

So, filling in the blank: The line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5, 5) \) is \( y = 25x - 120 \).

thats wrong

Apologies for the confusion in my previous response. Let's work through it step by step again to find the correct equation.

  1. Identify the slope: The original line is given as \( y = 25x + 1 \). The slope (m) of this line is \( 25 \).

  2. Use the point-slope form: We need a new line that is parallel to this one and passes through the point \( (5, 5) \). The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] where \( (x_1, y_1) \) is the point through which the line passes, and \( m \) is the slope.

  3. Substitute the values into the point-slope form:

    • \( m = 25 \)
    • \( (x_1, y_1) = (5, 5) \)

    Substituting these values gives: \[ y - 5 = 25(x - 5) \]

  4. Simplify this equation: \[ y - 5 = 25x - 125 \] \[ y = 25x - 120 \]

However, upon double-checking the calculations, I realize that everything seems consistent with the steps taken.

The final equation of the line that is parallel and passes through the point \( (5, 5) \) is: \[ y = 25x - 120 \]

If there's a specific part you believe is incorrect or if there's additional information I should consider, please let me know!