2.6 Quick Check Test Corrections-Math 8

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line descends from left to right.

Front

What is the effect of multiplying coordinates (x, y) by a factor of 2?

Back

Multiplying the coordinates (x, y) by 2 results in the new coordinates (2x, 2y), which scales the point away from the origin by a factor of 2.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope of the line, representing how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

How can you express the relationship between total cost and number of items purchased in a linear equation?

Back

The relationship can be expressed as t = mx + b, where t is the total cost, m is the cost per item, x is the number of items, and b is any fixed cost.

Front

What is the formula for a linear equation representing a total payment scenario?

Back

The formula is t = pm + b, where t is the total amount paid, p is the payment per period, m is the number of payments made, and b is the initial payment.

Front

What does the term 'initial payment' refer to in a payment plan?

Back

The initial payment is the upfront amount paid before any subsequent payments are made, often used to reduce the total amount financed.

Front

How do you interpret the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the function on the y-axis.

Front

What is the significance of the equation t = 5m + 75 in a payment scenario?

Back

This equation represents the total amount paid (t) as a function of the number of monthly payments (m), where $75 is the initial payment and $5 is the monthly payment.