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. instructions: if using your keyboard: 1. navigate to the text - entry field. 2. to access the wiris editor button, press alt + f10 for windows or option + fn + f10 for mac (if the function keys are enabled by default on your mac, just press option + f10). 3. press enter or return to open the wiris editor. 4. enter your wiris content. to save your wiris content, select the accept button. to exit without saving, select the cancel button or press esc. y = 3/2x + 1

Explanation:

Step1: Write the given equation in slope - intercept form

The given equation is $y=\frac{3}{2}x + 1$, where the slope - intercept form is $y=mx + b$ ($m$ is the slope and $b$ is the y - intercept), so $b = 1$.

Step2: Write the equation in standard form

The standard form of a linear equation is $Ax+By = C$. Starting from $y=\frac{3}{2}x + 1$, we subtract $\frac{3}{2}x$ from both sides to get $-\frac{3}{2}x+y=1$. Multiply through by 2 to clear the fraction: $-3x + 2y=2$. In the standard form $Ax + By=C$, $B = 2$.

Step3: Compare $b$ and $B$

Since $b = 1$ and $B = 2$, they are not equal.

Answer:

No, because in the slope - intercept form $y=\frac{3}{2}x + 1$, $b = 1$, and in the standard form $-3x + 2y=2$, $B = 2$.