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 of a line represent?

Back

The slope of a line 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

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

Back

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

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis. It is represented by the value of x when y = 0.

Front

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

Back

y = 3x - 2

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is a constant.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is a constant.

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 is the point-slope form of a linear equation?

Back

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