4.1 study guide

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 a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal.

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 y when x = 0.

Front

Write the equation of a line with a slope of 2 and a y-intercept of -3 in slope-intercept form.

Back

y = 2x - 3

Front

What is the equation of a line that passes through the points (1, 2) and (3, 6)?

Back

y = 2x.

Front

How do you convert the equation y = 3x + 4 into standard form?

Back

To convert to standard form, rearrange to get -3x + y = 4 or 3x - y = -4.

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

Write the equation of a line with a slope of -1 and passing through the point (4, 5).

Back

y = -1(x - 4) + 5 or y = -x + 9.

Front

What is the formula for finding the y-intercept from a linear equation in standard form Ax + By = C?

Back

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