What is the equation of a line with a slope of 2 and a y-intercept of -3?

What is the equation of 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 of a line can be expressed in the slope-intercept form, which is written as \(y = mx + b\), where \(m\) represents the slope and \(b\) is the y-intercept. In this case, the slope is given as 2, indicating that for every unit increase in \(x\), \(y\) increases by 2 units. The y-intercept is provided as -3, meaning that the line crosses the y-axis at the point (0, -3). Substituting these values into the slope-intercept form gives: \[ y = 2x - 3 \] This accurately represents a line that has a slope of 2 and crosses the y-axis at -3. Thus, the correct option reflects the proper relationship between the slope and y-intercept established in the equation.

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

In this case, the slope is given as 2, indicating that for every unit increase in (x), (y) increases by 2 units. The y-intercept is provided as -3, meaning that the line crosses the y-axis at the point (0, -3).

Substituting these values into the slope-intercept form gives:

[

y = 2x - 3

]

This accurately represents a line that has a slope of 2 and crosses the y-axis at -3. Thus, the correct option reflects the proper relationship between the slope and y-intercept established in the equation.