Writing Equations from two points (retake)

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.

Front

How do you find the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

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.

Front

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

Back

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

Front

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

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

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

Front

How can you convert the point-slope form to slope-intercept form?

Back

Rearrange the equation to solve for y: y = mx + (y1 - mx1).

Front

What is the equation of the line that passes through (0, 3) and (-4, -1)?

Back

The equation is y = 1x + 3.

Front

How do you determine if a given equation represents a line that passes through two points?

Back

Substitute the coordinates of the points into the equation and check if both satisfy it.

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.