Q. What is the slope of a line that is parallel to the line \(y = x + 2\)?

Q: What is the slope of a line parallel to y = x + 2?

The slope is 1, since y = mx + b has m=1 here; parallel lines have equal slopes.

Q: What is the slope of a line perpendicular to y = x + 2?

The slope is -1, the negative reciprocal of 1 (perpendicular slopes satisfy m_1 m_2 = -1).

Q: How do you write the equation of a line parallel to y = x + 2 through (3,4)?

Use slope 1: y-4=1(x-3), which simplifies to y = x + 1.

Q: How do you find the slope from two points (x_1,y_1) and (x_2,y_2)?

Slope is \frac{y_2-y_1}{x_2-x_1}. If this equals 1, the line is parallel to y = x + 2.

Q: How do you get the slope from standard form Ax+By=C?

Solve for y: y = -\frac{A}{B}x + \frac{C}{B}. The slope is -\frac{A}{B}.

Q: Does a parallel line share the same y-intercept as y = x + 2?

Does a parallel line share the same y-intercept as y = x + 2?

Q: What does slope 1 mean geometrically?

Slope 1 means rise equals run: the line makes a 45^\circ angle with the positive x-axis (since \tan 45^\circ = 1).

Q: How can you algebraically check two lines are parallel?

Put each in slope-intercept form y=mx+b. If their m-values are equal and b-values differ, the lines are parallel.

Answer

In slope-intercept form \(y=mx+b\) the slope is \(m\); for \(y=x+2\) we have \(m=1\), so any line parallel to it has slope \(1\).

Final answer: \(1\).

Detailed Explanation

Problem

Find the slope of a line that is parallel to the line \(y = x + 2\).

Step-by-step explanation

Recognize the slope-intercept form.

Lines written as \(y = mx + b\) are in slope-intercept form, where \(m\) is the slope and \(b\) is the y-intercept. What to do: identify the equation’s form and locate the coefficient of \(x\).
Identify the slope of the given line.

Compare \(y = x + 2\) to \(y = mx + b\). Rewrite explicitly as \(y = 1x + 2\). What to do: read off the coefficient of \(x\); here \(m = 1\).
Use the property of parallel lines.

For non-vertical lines in the plane, two lines are parallel if and only if they have the same slope. What to do: take the slope of the given line and use it for any line parallel to it.
State the slope of any line parallel to the given line.

Therefore, the slope of a line parallel to \(y = x + 2\) is \(1\).

Answer: The slope is \(1\).

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FAQs

What is the slope of a line parallel to \(y = x + 2\)?

The slope is 1, since \(y = mx + b\) has \(m=1\) here; parallel lines have equal slopes.

What is the slope of a line perpendicular to \(y = x + 2\)?

The slope is \(-1\), the negative reciprocal of 1 (perpendicular slopes satisfy \(m_1 m_2 = -1\)).

How do you write the equation of a line parallel to \(y = x + 2\) through \((3,4)\)?

Use slope 1: \(y-4=1(x-3)\), which simplifies to \(y = x + 1\).

How do you find the slope from two points \((x_1,y_1)\) and \((x_2,y_2)\)?

Slope is \(\frac{y_2-y_1}{x_2-x_1}\). If this equals 1, the line is parallel to \(y = x + 2\).

How do you get the slope from standard form \(Ax+By=C\)?

Solve for \(y\): \(y = -\frac{A}{B}x + \frac{C}{B}\). The slope is \(-\frac{A}{B}\).

Does a parallel line share the same y-intercept as \(y = x + 2\)?

What does slope 1 mean geometrically?

Slope 1 means rise equals run: the line makes a \(45^\circ\) angle with the positive x-axis (since \(\tan 45^\circ = 1\)).

How can you algebraically check two lines are parallel?

Put each in slope-intercept form \(y=mx+b\). If their \(m\)-values are equal and \(b\)-values differ, the lines are parallel.

Parallel to y=x+2, the slope is one.
The slope is 1.

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