Flashcard - Converting Standard and Point-Slope to Slope-Intercept

Front

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

Back

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

Front

How do you convert an equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What does the point-slope form of a linear equation look like?

Back

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

Front

How can you determine if a point lies on a given line represented by an equation?

Back

To determine if a point (x, y) lies on a line represented by an equation, substitute the x-value into the equation and check if the resulting y-value matches the y-coordinate of the point.

Front

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

Back

The slope (m) indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b) in the coordinate plane.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

Front

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

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the given point (x1, y1) and the slope m.