Forms of Linear Equations

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Identify the slope in the equation: y = mx + b.

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What does the term 'slope-intercept form' refer to?

Back

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

Front

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

Back

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

Front

Convert the equation y - 3 = 2(x - 1) to slope-intercept form.

Back

y = 2x + 1.

Front

What is the y-intercept in the equation y = 3x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other.

Front

Write the equation of a line in point-slope form that passes through (2, 3) with a slope of 4.

Back

y - 3 = 4(x - 2).