Linear Equations Test Review

Front

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

Back

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

Front

How do you identify the slope from a linear equation in slope-intercept form?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you determine the equation of a line given two points?

Back

To determine the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the meaning of the term 'rate of change' in the context of linear equations?

Back

The rate of change refers to the slope of the line, indicating how much y changes for a unit change in x.

Front

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

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as x increases, y also increases, representing a direct relationship between the two variables.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, representing an inverse relationship between the two variables.

Front

How can you find the equation of a line given its slope and a point on the line?

Back

Use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for calculating the cost in a linear cost model?

Back

The formula for calculating cost in a linear cost model is y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.