Question

What is the equation of the line that passes through the point (5,4) and has a slope of 2
Answer
its wrong
Answer
it needs to be y-?=2(x-?)
Answered by GPT-4o mini
To find the equation of a line that passes through a given point and has a specific slope, you can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope.

In this case, the point is (5, 4) and the slope \(m\) is 2. Plugging these values into the point-slope form gives:

\[
y - 4 = 2(x - 5)
\]

Now, simplify this equation:

1. Distribute the \(2\):
\[
y - 4 = 2x - 10
\]

2. Add \(4\) to both sides:
\[
y = 2x - 10 + 4
\]
\[
y = 2x - 6
\]

Thus, the equation of the line is:

\[
y = 2x - 6
\]
Answered by GPT-4o mini
Let's go through the calculation again step by step. We want to find the equation of a line that passes through the point \((5, 4)\) with a slope of \(2\).

Using the point-slope form of the line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

we can substitute \(m = 2\), \(x_1 = 5\), and \(y_1 = 4\):

\[
y - 4 = 2(x - 5)
\]

Now, let's distribute the slope on the right side:

\[
y - 4 = 2x - 10
\]

Next, we add \(4\) to both sides to isolate \(y\):

\[
y = 2x - 10 + 4
\]
\[
y = 2x - 6
\]

So the equation of the line is:

\[
y = 2x - 6
\]

If there’s a specific issue or misunderstanding you’re referring to, please let me know! This equation is indeed correct for a line passing through the point \((5, 4)\) with a slope of \(2\).
Answered by GPT-4o mini
Apologies for the confusion! If you want the equation in the point-slope form specifically, we can express it as you mentioned.

Using the point \((5, 4)\) and the slope \(m = 2\), the point-slope form can be written as:

\[
y - y_1 = m(x - x_1)
\]

Substituting in the values:

- \(y_1 = 4\)
- \(m = 2\)
- \(x_1 = 5\)

Substituting these values into the formula gives:

\[
y - 4 = 2(x - 5)
\]

So, in the format you are looking for, the equation can be written as:

\[
y - 4 = 2(x - 5)
\]

This is the correct point-slope form of the equation for the line that passes through the point \((5, 4)\) with a slope of \(2\).