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) 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 (b) represent in the equation y = mx + b?

Back

The y-intercept b represents the point where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the equation of the line that passes through (3, 3) and (4, -1)?

Back

The equation is y = -4x + 15.

Front

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

Back

1. Find the slope using the two points. 2. Use the slope and one point to find the y-intercept. 3. Write the equation in slope-intercept form.

Front

What is the formula to convert from point-slope form to slope-intercept form?

Back

Point-slope form is y - y1 = m(x - x1). To convert, solve for y to get y = mx + (y1 - mx1).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Given points (0, -2) and (-5, 3), what is the equation of the line?

Back

The equation is y = -x - 2.

Front

What is the significance of the coordinates in the points (x1, y1) and (x2, y2)?

Back

They represent two distinct points on the Cartesian plane used to determine the slope and equation of the line.

Front

How do you determine if a point lies on a line represented by an equation?

Back

Substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.