LT #7 Standard Form

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is represented as Ax + By = C, where A, B, and C are integers.

Front

What is the x-intercept of the line represented by the equation 2x + 3y = 6?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0. For the equation 2x + 3(0) = 6, the x-intercept is (3, 0).

Front

Identify the y-intercept of the equation 4x - 2y = 8.

Back

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0. For the equation 4(0) - 2y = 8, the y-intercept is (0, -4).

Front

What does the slope (m) represent in the slope-intercept form of a linear equation?

Back

In the slope-intercept form y = mx + b, the slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you convert the equation y = 2x + 3 into standard form?

Back

To convert y = 2x + 3 into standard form, rearrange it to -2x + y = 3 or 2x - y = -3.

Front

What is the slope of the line represented by the equation 3x + 4y = 12?

Back

To find the slope, convert to slope-intercept form: 4y = -3x + 12, so y = -\frac{3}{4}x + 3. The slope is -\frac{3}{4}.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0, indicating where the line crosses the y-axis.

Front

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

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect.

Front

What is the relationship between the slopes of perpendicular lines?

Back

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