What is the point-slope form of the equation of the line that has a slope of 2 and passes through the point (−5,4)

Question

(
−
5
,
4
)
?(1 point)
y−
y
−
=2
=
2
(x−
x
−
)

Answer 1

The point-slope form of the equation of a line is given by:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

Given a slope \( m = 2 \) and the point \( (-5, 4) \):

• \( x_1 = -5 \)
• \( y_1 = 4 \)

Plugging these values into the point-slope form equation:

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

Which simplifies to:

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

This is the point-slope form of the equation of the line.

Answer 2

the 5 is wrong

Answer 3

I apologize for any misunderstanding. Let’s clarify the point-slope form of the equation step by step again.

The point-slope form is given by:

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

where \( m \) is the slope and \((x_1, y_1)\) is a point on the line.

Given:

• Slope \( m = 2 \)
• Point \( (x_1, y_1) = (-5, 4) \)

Substituting these values into the formula gives:

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

Which simplifies to:

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

So the correct point-slope form of the equation of the line is:

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

If I misunderstood or you meant something different about the number "5," please clarify, and I'll be happy to help!

Answer 4

the (x+ 5) part is wrong

Answer 5

I apologize for the mistake! Let's correct the point-slope form of the equation accurately:

For the point-slope form:

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

Given:

• The slope \( m = 2 \)
• The point \( (x_1, y_1) = (-5, 4) \)

Substituting these values in, we have:

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

This simplifies as follows:

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

Now, to clarify:

When substituting \( x_1 = -5 \), we do indeed get \( x - (-5) \) which is the same as \( x + 5 \).

If you were referring to a different aspect or a specific detail, please let me know! As of now, the equation \( y - 4 = 2(x + 5) \) is correct based on the initial slope and point given.

Answer 6

ah so -5?

Answer 7

Yes! Let’s summarize it clearly.

Given:

• Slope: \( m = 2 \)
• Point: \( (x_1, y_1) = (-5, 4) \)

In the point-slope form of the line:

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

Substituting the slope and the coordinates of the point:

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

This simplifies to:

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

When you input the point \((-5, 4)\) into the formula, the equation correctly includes the term \( (x + 5) \) because \( x - (-5) = x + 5 \).

So overall, the point-slope form remains correct as:

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

If you were questioning specifically about how \(-5\) is being used in this context, yes, we keep the \(-5\) as gained from the coordinates of the point through which the line passes. Please let me know if you have any further questions!