Write the Equation of a Line Using Two Given Points

Front

What is the formula to find the slope (m) of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (2, 3) and (6, 7)?

Back

The slope (m) is m = (7 - 3) / (6 - 2) = 4 / 4 = 1.

Front

What is the y-intercept of a line in the slope-intercept form y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0.

Front

How do you write the equation of a line in slope-intercept form?

Back

The equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

Given the points (1, 2) and (3, 4), what is the equation of the line in slope-intercept form?

Back

First, find the slope: m = (4 - 2) / (3 - 1) = 1. Then use point-slope form: y - 2 = 1(x - 1) leads to y = x + 1.

Front

What is the point-slope form of a line?

Back

The point-slope form is given by 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 the point (4, 5), what is its equation?

Back

Using point-slope form: y - 5 = -2(x - 4) simplifies to y = -2x + 13.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

How do you find the y-intercept of a line given its slope and a point on the line?

Back

Use the slope-intercept form: b = y - mx, where (x, y) is the point on the line.