Represent Equations (y = mx + b)

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

What does the slope (m) represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how much y increases or decreases for each unit increase in x.

Front

What does the y-intercept (b) represent in the equation y = mx + b?

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 slope from a word problem involving a constant rate?

Back

The slope can be determined by identifying the constant rate of change described in the problem, often represented as 'per' something (e.g., dollars per day).

Front

If a taxi charges a flat fee plus a per-mile rate, how would you write the equation?

Back

The equation would be in the form y = mx + b, where m is the per-mile rate and b is the flat fee.

Front

In the equation y = -2x + 40, what does the negative slope indicate?

Back

The negative slope indicates that as x increases, y decreases, showing a decrease in the quantity represented by y.

Front

How do you identify the initial amount in a situation described by a linear equation?

Back

The initial amount is represented by the y-intercept (b) in the equation y = mx + b.

Front

What is the equation for a situation where a person spends a fixed amount each month from a gift card?

Back

The equation would be y = -mx + b, where m is the amount spent each month and b is the initial amount on the gift card.

Front

How can you convert a word problem into a linear equation?

Back

Identify the quantities involved, determine the relationship (constant rate), and express it in the form y = mx + b.

Front

What is the significance of the coefficients in the equation y = mx + b?

Back

The coefficient m represents the slope (rate of change), and the constant b represents the initial value (y-intercept).