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.

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).

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 (x1, y1) and (x2, y2), how do you write the equation of the line?

Back

1. Calculate the slope m using m = (y2 - y1) / (x2 - x1). 2. Use the slope and one point to find the y-intercept b. 3. Write the equation in the form y = mx + b.

Front

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

Back

y = x + 3.

Front

What is the equation of the line that passes through (6, 3) and (4, 1)?

Back

y = 1x - 3.

Front

How do you determine if two points create a positive or negative slope?

Back

If y2 - y1 > 0, the slope is positive; if y2 - y1 < 0, the slope is negative.

Front

What is the equation of the line that passes through (0, -2) and (-5, 3)?

Back

y = -x - 2.

Front

What is the equation of the line that goes through the points (2, 9) and (3, 1)?

Back

y = -8x + 25.

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.