12.2 Daily Grade - Solve for a variable, y-int, and zero

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 convert the equation 6x - 2y = 12 to slope-intercept form?

Back

To convert to slope-intercept form, isolate y: 6x - 2y = 12 -> -2y = -6x + 12 -> y = 3x - 6.

Front

What does the slope (m) represent in the slope-intercept form?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in the slope-intercept form?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

How do you find the y-intercept from the equation 3x + 2y = 5?

Back

Set x = 0: 3(0) + 2y = 5 -> 2y = 5 -> y = 2.5, so the y-intercept is (0, 2.5).

Front

What is the zero of a function?

Back

The zero of a function is the x-value where the function equals zero, represented as (x, 0).

Front

How do you find the zero of the function represented by the equation 2y = 6x - 12?

Back

Set y = 0: 2(0) = 6x - 12 -> 0 = 6x - 12 -> 6x = 12 -> x = 2, so the zero is (2, 0).

Front

What is the significance of the point (4, 0) on a graph?

Back

The point (4, 0) indicates that when x = 4, the value of the function is zero, meaning it crosses the x-axis at this point.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the relationship between the slope and parallel lines?

Back

Parallel lines have the same slope; if two lines have equal slopes, they will never intersect.