Slope Intercept & Point Slope Flashcard

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

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 is the slope of the line passing through the points (-3, 6.9) and (3.5, -0.9)?

Back

m = -1.2.

Front

What is the slope of the line represented by the equation y = x + 4?

Back

m = 1.

Front

What is point-slope form of a linear equation?

Back

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

Front

What is the equation in point-slope form for a line with slope 4 passing through (1, -1)?

Back

y + 1 = 4(x - 1).

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

What is the slope of the line represented by the equation y = -\frac{4}{3}x - 2?

Back

m = -\frac{4}{3}.

Front

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

Back

To convert, solve for y in the point-slope equation to get it into the form y = mx + b.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, growth, or decline in various contexts.