Linear Equations, Graphs, and Tables Flashcard

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

How do you find 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 does the y-intercept represent in a linear equation?

Back

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

Front

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

Back

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

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 convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a line passes through the points (1, 2) and (3, 6), what is its equation?

Back

First, find the slope: m = (6 - 2) / (3 - 1) = 2. Then use point-slope form: y - 2 = 2(x - 1) which simplifies to y = 2x.

Front

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

Back

The coefficient m represents the slope of the line, while b represents the y-intercept.

Front

How do you interpret the equation y = -3x + 4?

Back

This equation has a slope of -3, indicating a decrease in y as x increases, and a y-intercept of 4.