Writing Equations Bonus Flashcard

Front

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

Back

The slope-intercept form is given by the equation 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 = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

If a line has a slope of 2/3, what does this indicate about the line's steepness?

Back

A slope of 2/3 indicates that for every 3 units moved horizontally, the line rises 2 units vertically.

Front

How do you convert the equation y = 4x + 3 into standard form?

Back

To convert to standard form, rearrange to Ax + By = C: -4x + y = 3.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 5?

Back

The equation is y = -1x + 5.

Front

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

Back

First, calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use point-slope form: y - y1 = m(x - x1).

Front

What is the significance of the delivery fee in the equation y = 30 + 12.50x?

Back

The delivery fee of $30 is a fixed cost added to the total cost of the meal for x people.

Front

How do you determine if a line is increasing or decreasing based on its slope?

Back

If the slope is positive, the line is increasing; if negative, the line is decreasing.

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.