Equation of a Line

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 find the slope between 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 3/10, what does this indicate about the line's steepness?

Back

A slope of 3/10 indicates that for every 10 units moved horizontally, the line rises 3 units vertically, showing a gentle incline.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept, indicating the value of y when x is 0.

Front

How can you determine if a point is a y-intercept from its coordinates?

Back

A point is a y-intercept if its x-coordinate is 0, represented as (0, b).

Front

What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot, minimizing the distance from all points to the line.

Front

How do you write the equation of a line given two points?

Back

First, calculate the slope using the two points, then use the point-slope form to write the equation.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, showing a downward trend.

Front

What is the formula for the slope of a line passing through points (x1, y1) and (x2, y2)?

Back

The formula is m = (y2 - y1) / (x2 - x1).