Forms of Linear Equations

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 the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What does the slope (m) represent in a linear equation?

Back

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

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

Write the slope-intercept form of the equation with slope 4 and y-intercept 3.

Back

y = 4x + 3.

Front

What is point-slope form of a linear equation?

Back

Point-slope form is given by the equation y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

Convert the point-slope equation y - 5 = -6(x + 2) to slope-intercept form.

Back

y = -6x - 12 + 5, which simplifies to y = -6x - 7.

Front

If a line has a slope of -1 and passes through the point (2, 3), what is its equation in point-slope form?

Back

y - 3 = -1(x - 2).

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other (m1 * m2 = -1).