cl 2 - 114. identify ( m ) and ( b ) in the following equations. what do ( m ) and ( b ) represent?\n\n a. (…

Answer:

a. (m = 2), (b = 1) b. (m=\frac{2}{5}), (b=- 4)

Explanation:

Step1: Recall the slope - intercept form of a linear equation

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

Step2: Identify (m) and (b) for equation (y = 2x+1)

Comparing (y = 2x + 1) with (y=mx + b), we can directly see that (m = 2) (the coefficient of (x)) and (b = 1) (the constant term).

Step3: Identify (m) and (b) for equation (y=\frac{2}{5}x - 4)

Comparing (y=\frac{2}{5}x-4) with (y = mx + b), we find that (m=\frac{2}{5}) (the coefficient of (x)) and (b=-4) (the constant term).

In the slope - intercept form (y = mx + b), (m) represents the slope of the line (a measure of the steepness of the line, calculated as (\frac{\text{rise}}{\text{run}})) and (b) represents the (y) - intercept (the point ((0,b)) where the line crosses the (y) - axis).