WU: 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) between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula 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 the points (0, -2) and (-5, 3), what is the slope of the line?

Back

The slope m = (3 - (-2)) / (-5 - 0) = 5 / -5 = -1.

Front

What is the equation of the line in slope-intercept form that passes through (0, -2) with a slope of -1?

Back

The equation is y = -1x - 2 or y = -x - 2.

Front

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

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 - mx1).

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 -3 and passes through the point (1, 1), what is its equation in point-slope form?

Back

The equation is y - 1 = -3(x - 1).

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.

Front

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

Back

Two lines are parallel if they have the same slope (m).