Linear Equations Lecture Notes

These flashcards cover key concepts and definitions related to linear equations, including slope-intercept form, point-slope form, and methods for obtaining equations from given points.

What is the general form of a linear equation in slope-intercept form?

y = mx + b, where m is the slope and b is the y-intercept.

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

m = (y2 - y1) / (x2 - x1).

What is the slope-intercept form of the linear equation if the slope is -4 and the y-intercept is 3?

y = -4x + 3.

Write the equation in slope-intercept form for a line that passes through points (3, -5) and (6, 4).

y = 3x - 14.

What does point-slope form of a linear equation look like?

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

Given the slope -3 and the y-intercept 4, what is the equation in slope-intercept form?

y = -3x + 4.

How would you convert the equation 3x - 2y = 8 to slope-intercept form?

y = (3/2)x - 4.

What does it mean for two lines to be parallel?

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

If a line has a slope of 0, what does that indicate about the line?

A slope of 0 indicates a horizontal line.

What does it mean for two lines to be perpendicular?

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