Parallel & Perpendicular Lines Practice

Question

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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

Answer 1

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 $y=25x-120$.

Answer 2

thats wrong

Answer 3

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!