Algebra-Unit 6 -(Lessons 1-6)Flashcard Review

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 the y-intercept represent in a linear equation?

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 y = mx + b.

Front

How can you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope (m) is positive and decreasing if the slope is negative.

Front

What is the equation of a line with a slope of 1 and a y-intercept of 0?

Back

The equation is y = 1x + 0 or simply y = x.

Front

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

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1). Substitute the slope and the coordinates of the point.

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; a positive slope rises, while a negative slope falls.

Front

How can you check if a point lies on the graph of a linear equation?

Back

Substitute the x-coordinate of the point into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is the equation of a line that passes through the origin with a slope of -2?

Back

The equation is y = -2x.