Finding Slope and Intercepts Flashcard

Front

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

The point-slope form 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 point-slope form to slope-intercept form?

Back

To convert, solve for y: y = mx + b, where b is the y-intercept.

Front

What is the y-intercept of a line?

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

Given the points (1, 2) and (3, 6), what is the slope of the line?

Back

The slope is m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2.

Front

What is the equation of the line in point-slope form using the points (0, 0) and (5, 10)?

Back

The equation is y - 0 = 2(x - 0).

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and use the formula m = \frac{rise}{run}.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.