Writing Equations of Lines

Front

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

Back

The slope-intercept form of a linear equation is given by 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

How do you determine the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in the equation of a line?

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 equation of a line given its slope and a point on the line?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Tags

CCSS.8.EE.B.5

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Tags

CCSS.8.EE.B.5

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the formula for finding the equation of a line that passes through two points?

Back

First, calculate the slope using m = (y2 - y1) / (x2 - x1). Then use the point-slope form to write the equation.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero in the slope formula.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0 because there is no change in y as x changes.

Tags

CCSS.8.EE.B.5