Which of the following equations represents a line with a slope of 2 and a y-intercept of -3?

Which of the following equations represents a line with a slope of 2 and a y-intercept of -3?

• A. y = 2x + 3
• B. y = 2x - 3
• C. y = -2x + 3
• D. y = -2x - 3

Answer: (B)

The equation that represents a line can be expressed in the slope-intercept form, which is given as \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. In the question, it specifies a slope of 2 and a y-intercept of -3. By substituting these values into the slope-intercept form, you would have: - The slope \( m \) is 2, so you write \( 2x \). - The y-intercept \( b \) is -3, so you write \(-3\). Combining these gives the equation \( y = 2x - 3 \). This indicates that the line rises by 2 units for every 1 unit it moves to the right (reflecting the slope) and crosses the y-axis at -3 (the y-intercept). Thus, the equation that correctly represents the line described by these characteristics is indeed \( y = 2x - 3 \). This aligns perfectly with the provided values of slope and y-intercept.

The equation that represents a line can be expressed in the slope-intercept form, which is given as ( y = mx + b ), where ( m ) represents the slope and ( b ) represents the y-intercept.

In the question, it specifies a slope of 2 and a y-intercept of -3. By substituting these values into the slope-intercept form, you would have:

• The slope ( m ) is 2, so you write ( 2x ).

• The y-intercept ( b ) is -3, so you write (-3).

Combining these gives the equation ( y = 2x - 3 ). This indicates that the line rises by 2 units for every 1 unit it moves to the right (reflecting the slope) and crosses the y-axis at -3 (the y-intercept).

Thus, the equation that correctly represents the line described by these characteristics is indeed ( y = 2x - 3 ). This aligns perfectly with the provided values of slope and y-intercept.