Question

is the b in slope - intercept form equivalent to the b in standard form, ax + by = c? if yes, explain your reasoning. if no, provide a counterexample. -3x+2y = 2, b = 2. sample answer: no; in y = x + 5, b = 5. in standard form, the equation is x - y=-5, so b=-1. completed. a sample answer is available above.

Explanation:

Step1: Convert slope - intercept to standard form

The slope - intercept form is $y=mx + b$. Given the general form of the equation in standard form is $Ax+By = C$. Starting from $y=mx + b$, we can rewrite it as $-mx+y=b$.

Step2: Analyze the coefficients

For the equation $-3x + 2y=2$, comparing with $Ax+By = C$, we have $A=-3$, $B = 2$, $C = 2$. In slope - intercept form $y=mx + b$, if we solve $-3x + 2y=2$ for $y$, we get $2y=3x + 2$ or $y=\frac{3}{2}x+1$. Here $b = 1$.
The value of $B$ in standard form ($-3x + 2y=2$) is 2 and $b$ in slope - intercept form ($y=\frac{3}{2}x + 1$) is 1.

Answer:

No, because when we convert the standard - form equation $-3x + 2y=2$ to slope - intercept form $y=\frac{3}{2}x + 1$, the $b$ value (y - intercept) is 1 and the $B$ value in standard form is 2.