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

What is the y-intercept in 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

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 slope-intercept form of a linear equation?

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 write an equation from a word problem involving a cost?

Back

Identify the fixed cost and the variable cost per unit. Use the form y = fixed cost + (variable cost per unit)x.

Front

What is the equation for a line with a slope of 2 that passes through the point (1, 3)?

Back

Using the point-slope form, the equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

What does it mean if a slope is negative?

Back

A negative slope indicates that as x increases, y decreases. The line goes downwards from left to right.

Front

How can you determine if a point lies on a line represented by an equation?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

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.