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 find the equation of a line given a slope and a point?

Back

To find the equation of a line given a slope (m) and a point (x1, y1), use the point-slope form: y - y1 = m(x - x1). You can then rearrange it to slope-intercept form.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x; it indicates how steep the line is and the direction it goes (positive slope means it rises, negative slope means it falls).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you convert the 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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

In real-world applications, the slope can represent rates such as speed, cost per item, or any other ratio of change between two quantities.

Tags

CCSS.8.EE.B.5

Front

How do you determine the slope from two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line with a slope of 0?

Back

The equation of a line with a slope of 0 is a horizontal line, represented as y = b, where b is the y-value for all x.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-value for all y.

Front

How do you find the slope from the equation of a line in standard form?

Back

To find the slope from the standard form Ax + By = C, rearrange it to slope-intercept form (y = mx + b) to identify m.

Tags

CCSS.8.EE.B.5