Writing Equations of Lines

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation 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 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 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

If a line has a slope of 0, what does that indicate about the line?

Back

A line with a slope of 0 is horizontal, meaning it does not rise or fall as it moves along the x-axis.

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Tags

CCSS.8.EE.B.5

Front

How can you find the equation of a line given a point and a slope?

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 formula for converting the standard form of a line Ax + By = C to slope-intercept form?

Back

To convert 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 does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and use the formula m = rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line with a slope of 3 and a y-intercept of 5?

Back

The equation of the line is y = 3x + 5.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3