Reteach LE.A.2 Graphing Lines & Writing Equations

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope 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 slope-intercept form y = mx + b.

Front

How can you graph the equation 2x + 4y = 4?

Back

To graph, first convert to slope-intercept form: 4y = -2x + 4, then y = -1/2x + 1. Plot the y-intercept (0,1) and use the slope -1/2 to find another point.

Front

What is the equation of a line with a slope of 3 that passes through the point (1, 2)?

Back

Using the point-slope form, the equation is y - 2 = 3(x - 1), which simplifies to y = 3x - 1.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert the equation y = 4x - 1 to standard form?

Back

Rearranging gives -4x + y = -1, or 4x - y = 1.

Front

What is the significance of parallel lines in graphing?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect.

Front

What is the significance of perpendicular lines in graphing?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.

Front

How do you write the equation of a line given two points (6,3) and (4,1)?

Back

First, find the slope: m = (1 - 3) / (4 - 6) = 1. Then use point-slope form: y - 3 = 1(x - 6), which simplifies to y = x - 3.