Equation of a Line

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is 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 the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line steep.

Front

What is the significance of a negative slope in a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How can you determine if a line is vertical or horizontal?

Back

A vertical line has an undefined slope and is represented by the equation x = a constant. A horizontal line has a slope of 0 and is represented by the equation y = a constant.

Front

What is the formula for finding the equation of a line given a point and the slope?

Back

The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/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, showing the trend of the data.

Front

How can you use a trend line to make predictions?

Back

You can use a trend line to predict values by extending the line and finding the corresponding y-value for a given x-value.