Unit 4 - Linear Equations Study Guide

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope of m1, and the other has a slope of m2, then m1 * m2 = -1.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) 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 y when x = 0.

Front

What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot, used to predict values.

Front

How do you write an equation of a line given a point and a 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 significance of the coefficients in the equation of a line?

Back

The coefficients in the equation of a line indicate the slope and the y-intercept, determining the line's steepness and position.

Front

How can you identify parallel lines from their equations?

Back

Parallel lines have the same slope. If two lines are in the form y = mx + b, they are parallel if their m values are equal.

Front

What is the formula for finding the equation of a line perpendicular to a given line?

Back

To find the equation of a line perpendicular to a given line with slope m, use the negative reciprocal of m, which is -1/m.