8.5I Flashcard

Front

What is the algebraic equation for a linear relationship represented in a table?

Back

The algebraic equation can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you express the total amount of money saved over time with a starting amount and a constant weekly saving?

Back

The total amount saved can be expressed as t = mw + b, where m is the amount saved per week, w is the number of weeks, and b is the initial amount saved.

Front

What does 'slope' represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how much y increases or decreases as x increases.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the equation y = 4x - 21?

Back

In the equation y = 4x - 21, the slope (m) is 4.

Front

What is the y-intercept in the equation y = -5/2x - 1?

Back

The y-intercept (b) in the equation y = -5/2x - 1 is -1.

Front

How can 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 isolate it on one side of the equation.

Front

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

Back

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

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.