8.5I-Writing Equations in the Form y=mx+b (Verbal)

Front

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

Back

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

Front

In the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, indicating how steep the line is and the direction it goes (positive or negative).

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you write an equation for a situation where a fixed cost is added to a variable cost?

Back

You write the equation in the form y = mx + b, where 'b' is the fixed cost and 'm' is the variable cost per unit.

Front

If a concert ticket costs $30 and there is a $10 service fee, how would you write the equation for the total cost y in terms of the number of tickets x?

Back

The equation would be y = 30x + 10.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

How can you determine the y-intercept from a linear equation?

Back

The y-intercept can be determined by setting x = 0 in the equation and solving for y.

Front

Write an equation for a situation where a water tank starts with 100 gallons and loses water at a rate of 5 gallons per hour.

Back

The equation would be y = -5x + 100.

Front

What is the significance of the y-intercept in real-world problems?

Back

The y-intercept often represents the starting value or initial condition of a situation before any changes occur.

Front

If a car rental service charges $50 per day plus a one-time fee of $20, how would you express the total cost y for x days?

Back

The equation would be y = 50x + 20.