Q. What is the slope in the equation \(y = 2x + 3\)?

Q: What is the slope of y=2x+3?

The slope is the coefficient of x: 2. It means for every 1 unit right, y increases by 2.

Q: How does this relate to the form y=mx+b?

In y=mx+b, m is the slope and b is the y-intercept. Here m=2 and b=3.

Q: What is the y-intercept of y=2x+3?

The y-intercept is 3, the point (0,3) where the line crosses the y-axis.

Q: How do you graph the slope 2 quickly?

From (0,3) move up 2 (rise) and right 1 (run) to get another point (1,5), then draw the line through them.

Q: What is the slope of a horizontal or vertical line?

horizontal line has slope 0. vertical line has undefined slope because run =0 makes division by zero.

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

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

Q: What is the slope of a line parallel to y=2x+3?

Any line parallel has the same slope 2; e.g., y=2x+7 is parallel.

Answer

In slope-intercept form \[ y = mx + b \] the slope is \(m\). Comparing with \[ y = 2x + 3 \] gives \[ m = 2. \]

Detailed Explanation

Solution — Find the slope of the line

Recognize the form of the equation.

The equation is in slope‑intercept form, which is written as
\( y = m x + b \), where \( m \) denotes the slope and \( b \) denotes the y‑intercept.
Identify the slope from the given equation.

The given equation is
\( y = 2x + 3 \).
By comparison with \( y = m x + b \), the coefficient of \( x \) is the slope:
\( m = 2 \).
Interpret the slope quantitatively.

Writing the slope as a ratio,
\( m = 2 = \dfrac{2}{1} \).
This means that for every increase of \( 1 \) unit in \( x \), \( y \) increases by \( 2 \) units.
In terms of differences,
\( \dfrac{\Delta y}{\Delta x} = 2 \).
Verify using two points on the line.

Take two points: when \( x = 0 \), \( y = 3 \) so the point is \( (0,3) \); when \( x = 1 \), \( y = 5 \) so the point is \( (1,5) \).
Compute the slope between them:
\( \dfrac{5 – 3}{1 – 0} = \dfrac{2}{1} = 2 \).
This confirms the value above.

Final answer: The slope is \( 2 \).

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FAQs

What is the slope of \(y=2x+3\)?

The slope is the coefficient of \(x\): \(2\). It means for every 1 unit right, \(y\) increases by 2.

How does this relate to the form \(y=mx+b\)?

In \(y=mx+b\), \(m\) is the slope and \(b\) is the y-intercept. Here \(m=2\) and \(b=3\).

What is the y-intercept of \(y=2x+3\)?

The y-intercept is \(3\), the point \((0,3)\) where the line crosses the y-axis.

How do you graph the slope 2 quickly?

From \((0,3)\) move up 2 (rise) and right 1 (run) to get another point \((1,5)\), then draw the line through them.

What is the slope of a horizontal or vertical line?

horizontal line has slope \(0\). vertical line has undefined slope because run \(=0\) makes division by zero.

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

What is the slope of a line parallel to \(y=2x+3\)?

Any line parallel has the same slope 2; e.g., \(y=2x+7\) is parallel.

What is the slope of a line perpendicular to \(y=2x+3\)?

Perpendicular slopes are negative reciprocals. The perpendicular slope is \(-\frac{1}{2}\).

The slope of y = 2x + 3 is exactly 2.
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