Linear Equations Test

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the average rate of change of a function?

Back

The average rate of change is calculated as (f(b) - f(a)) / (b - a) over the interval [a, b].

Front

What is the equation of a line with a slope of 3 that passes through the point (1, 2)?

Back

The equation is y = 3x - 1.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

Rearrange the equation Ax + By = C to solve for y, resulting in y = (-A/B)x + (C/B).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope rises, while a negative slope falls.

Front

What is the formula for the slope of a line given its equation in standard form?

Back

For the equation Ax + By = C, the slope is -A/B.