Writing Equations from two points

Front

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

Back

The slope-intercept form is 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 slope (m) from two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

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, represented by the value of b in the equation y = mx + b.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Given points (0, 3) and (-4, -1), what is the slope of the line?

Back

The slope m = (-1 - 3) / (-4 - 0) = -4 / -4 = 1.

Tags

CCSS.8.EE.B.5

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), then rearrange to slope-intercept form.

Front

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

Back

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

Front

If a line has a slope of -2 and passes through (1, 4), what is its equation?

Back

Using point-slope form: y - 4 = -2(x - 1) simplifies to y = -2x + 6.

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 rises, while a negative slope falls.

Tags

CCSS.8.EE.B.5

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Tags

CCSS.8.EE.B.6

Front

What is the formula to convert from standard form Ax + By = C to slope-intercept form?

Back

Solve for y: y = (-A/B)x + (C/B).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3