Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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. It indicates how steep the line is and the direction it goes (positive or negative).

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. It represents the value of y when x is 0.

Front

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

Back

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

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

How do you convert the equation y = 3x - 2 into slope-intercept form?

Back

The equation is already in slope-intercept form, which is y = mx + b.

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope is -4.

Front

What is the y-intercept of the equation y = 1/2x + 6?

Back

The y-intercept is 6.

Front

If a line passes through the points (1, 2) and (3, 6), what is its equation?

Back

First, find the slope: m = (6 - 2) / (3 - 1) = 2. Then use point-slope form: y - 2 = 2(x - 1) which simplifies to y = 2x.

Front

What is the standard form of a linear equation?

Back

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