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.

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5