(MCA) 4.3 (Flashcard) Graphing and Writing linear equations.

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 of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is 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, represented as (0, b) in the equation y = mx + b.

Front

If a line has a slope of 4, what does this indicate about the line's steepness?

Back

A slope of 4 indicates that for every 1 unit increase in x, the value of y increases by 4 units, making the line steep.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 3?

Back

The equation is y = -1x + 3.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the significance of the point (0, b) in the slope-intercept form?

Back

The point (0, b) is the y-intercept of the line, indicating where the line crosses the y-axis.

Front

What is the equation of a line that passes through the points (2, 3) and (4, 7)?

Back

First, find the slope: m = (7 - 3) / (4 - 2) = 2. Then use point-slope form: y - 3 = 2(x - 2) or y = 2x - 1.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the formula to convert from standard form Ax + By = C to slope-intercept form?

Back

To convert, solve for y: y = (-A/B)x + (C/B).