3.3 & 3.4 Slope Intercept and Point Slope

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented by '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 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-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula: y = mx + b, where m is the slope and b is the y-intercept.

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 from point-slope form 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 of the equation.

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 b in the slope-intercept form (y = mx + b).

Front

How can you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from a linear equation in standard form (Ax + By = C), set x = 0 and solve for y.

Front

What is the relationship between the slope of a line and its steepness?

Back

A positive slope indicates the line rises from left to right, while a negative slope indicates it falls. The greater the absolute value of the slope, the steeper the line.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form (y = mx + b), start at the y-intercept (0, b) and use the slope (rise/run) to find another point on the line.

Front

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

Back

The slope can represent rates of change, such as speed, cost per item, or any other relationship where one quantity changes in relation to another.