Linear forms

Front

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

Back

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

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

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 convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope equation y - y1 = m(x - x1) to get y = mx + (y1 - mx1).

Front

What is the standard form of a linear equation?

Back

The standard form is given by Ax + By = C, where A, B, and C are integers and A should be non-negative.

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 y when x = 0.

Front

How can you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) for points (x1, y1) and (x2, y2).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the significance of the coefficients A and B in the standard form of a linear equation?

Back

A and B represent the direction and steepness of the line; they determine how the line behaves in relation to the axes.

Front

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

Back

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