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 (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

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

If the slope of a line is m, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to it is -1/m.

Front

What is the y-intercept of the line represented by the equation y = 4x + 3?

Back

The y-intercept is 3, which is the value of y when x = 0.

Front

How do you convert the standard form of a linear equation Ax + By = C to slope-intercept form?

Back

To convert, solve for y: y = (-A/B)x + (C/B).

Front

What is the equation of a line that passes through the point (2, 3) with a slope of 4?

Back

The equation is y - 3 = 4(x - 2), which simplifies to y = 4x - 5.

Front

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

Back

The slope indicates the steepness of the line and the direction it moves: positive slope goes up, negative slope goes down.

Front

How can you determine if two lines are neither parallel nor perpendicular?

Back

If the slopes of the two lines are different and their product is not -1, they are neither parallel nor perpendicular.