All 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

What is slope-intercept form?

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

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

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is 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 = 2x + 3 to standard form.

Back

The standard form is -2x + y = 3.

Front

What is the y-intercept of the equation y = 4x - 7?

Back

The y-intercept is -7, which is the point where the line crosses the y-axis.

Front

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

Back

Rearrange the equation to get Ax + By = C, ensuring A, B, and C are integers.

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y = 0.

Front

Write the equation of a line with slope 3 passing through the point (2, 5) in point-slope form.

Back

y - 5 = 3(x - 2).