Writing Equations from Graphs

Front

What is the slope of a line?

Back

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

Tags

CCSS.8.EE.B.5

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. In the equation y = mx + b, 'b' represents the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you write the equation of a line given two points?

Back

To write the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m = (y2 - y1) / (x2 - x1)). Then use the point-slope form: y - y1 = m(x - x1).

Front

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

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope (m) is positive, and it is decreasing if the slope (m) is negative.

Tags

CCSS.8.EE.B.5

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They will never intersect.

Tags

CCSS.8.EE.B.5

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means one slope is the negative reciprocal of the other.

Tags

CCSS.8.EE.B.6

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept of a linear equation, set y = 0 and solve for x.

Front

What is the significance of the coefficients in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' is the slope of the line, and 'b' is the y-intercept, indicating where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3