Question

define the y-intercept in a linear equation and the slope.

a. the y-intercept is where the graph of the linear equations begins on the x-axis and the slope is the rate of change.

b. the y-intercept is where the graph of the linear equations begins on the y-axis and the slope is the constant rate of change.

c. the slope is where the graph of the linear equations begins on the y-axis and the y-intercept is the rate of change.

submit answer

Explanation:

To determine the correct option, we analyze the definitions of y - intercept and slope in a linear equation. The y - intercept of a linear equation (in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept) is the value of \(y\) when \(x = 0\), which means it is the point where the graph intersects the y - axis. The slope represents the constant rate of change of \(y\) with respect to \(x\) (for a linear function, the rate of change is constant).

• Option A: The y - intercept is not on the x - axis (the x - intercept is on the x - axis), so this option is incorrect.
• Option B: It correctly states that the y - intercept is where the graph meets the y - axis and the slope is the constant rate of change.
• Option C: It swaps the definitions of slope and y - intercept, so this option is incorrect.

Answer:

B. The y - intercept is where the graph of the linear equations begins on the y - axis and the slope is the constant rate of change.