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 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.

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.

Front

How can you find the slope of a line given 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 identify the slope and y-intercept from the equation y = 3x + 5?

Back

In the equation y = 3x + 5, the slope (m) is 3 and the y-intercept (b) is 5.

Front

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

Back

Parallel lines have the same slope but different y-intercepts.

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 has a slope of -1/m.

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), substituting the given point (x1, y1) and the slope (m).

Front

What is the formula for finding the y-coordinate of a point on a line given its x-coordinate?

Back

Substitute the x-coordinate into the line's equation to find the corresponding y-coordinate.