Slope Flashcard

Front

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

Back

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

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is and the direction it goes (positive or negative).

Front

How can you determine the slope from two points?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

Front

How do you find a point on a line given its equation in point-slope form?

Back

To find a point on a line given its equation in point-slope form, you can choose any value for x and solve for y using the equation.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other will have a slope of -1/m.

Front

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

Back

To write the equation of a line given a point (x1, y1) and a slope m, use the point-slope form: y - y1 = m(x - x1).

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).