Linear Equations from Slope and Point 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 calculate 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 slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

The point-slope form is given by the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

How can you convert the point-slope form to slope-intercept form?

Back

To convert, solve for y: y = mx - mx1 + y1.

Front

What is the equation of a line with a slope of 0?

Back

The equation is y = b, where b is the y-value of the line, indicating a horizontal line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is x = a, where a is the x-value of all points on the line.

Front

How do you find 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.