Writing Equations 8.5I

Front

What is the general form of a linear equation?

Back

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

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What does 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0.

Front

How do you determine 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 of the line represented by the equation y = -1x + 2?

Back

The slope of the line represented by the equation y = -1x + 2 is -1.

Front

If a plant is 5 cm tall and grows at a rate of 3 cm per month, what is the equation representing its height after x months?

Back

The equation representing the plant's height after x months is y = 5 + 3x.

Front

What is the meaning of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, representing a downward trend.

Front

How can you write an equation from a word problem involving a constant rate of change?

Back

Identify the initial value and the rate of change, then use the formula y = initial value + (rate of change * x) to write the equation.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept indicates the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How do you interpret the slope in a real-world context?

Back

The slope represents the rate of change between the two variables, indicating how much one variable changes for a unit change in the other.