9/29 - Slope and Equation of a Line

Front

What is the slope of a line?

Back

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

Front

How do you calculate the slope given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

Find the slope given the points (2, −7) and (−1, 6).

Back

The slope is -13/3.

Front

Find the slope of a line that rises 4 units for every 3 units it runs to the right.

Back

The slope is 4/3.

Front

What is the slope-intercept form of a line?

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

Identify the slope in the equation y = 2x - 2.

Back

The slope is 2.

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 'b' in the slope-intercept form.

Front

Write the equation of the line with a slope of -3 and a y-intercept of -3.

Back

The equation is y = -3x - 3.

Front

What is the equation of a line that has a slope of 4/3 and passes through the point (0, 2)?

Back

The equation is y = (4/3)x + 2.

Front

How do you determine the equation of a line from a graph?

Back

Identify the slope and the y-intercept from the graph, then use the slope-intercept form y = mx + b.