If C=24 what values of A and B complete Ax+By=C for each graph? Write the standard form for each equation. a. b. The standard form of the equation for part (a) is 6x-8y=24 b. For the graph in part (b), the value for A is square and the value for B is square

To find the values of \(A\) and \(B\) that complete the equation \(A x + B y = C\) for the graph described, we need to determine the slope of the line and use the points through which it passes.Step 1: Find the slope of the line.The slope (m) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:\[m = \frac{y_2 - y_1}{x_2 - x_1}\]Using the points (0,2) and (3,0) from the picture details:\[m = \frac{0 - 2}{3 - 0} = \frac{-2}{3}\]Step 2: Write the slope-intercept form of the equation.The slope-intercept form is \(y = mx + b\), where \(b\) is the y-intercept.Using the slope we found and the y-intercept from the point (0,2):\[y = -\frac{2}{3}x + 2\]Step 3: Convert to standard form.The standard form of a linear equation is \(Ax + By = C\). To convert the slope-intercept form to standard form, we need to eliminate the fraction and rearrange the terms:\[y = -\frac{2}{3}x + 2\]\[\frac{2}{3}x + y = 2\]To eliminate the fraction, multiply every term by 3:\[2x + 3y = 6\]Step 4: Adjust the equation to match \(C = 24\).To make the constant term equal to 24, we need to multiply the entire equation by a factor that will make the constant term 24. Since the constant term is currently 6, we multiply the entire equation by 4:\[4(2x + 3y) = 4(6)\]\[8x + 12y = 24\]Now we have the equation in standard form with \(C = 24\).Step 5: Compare with the given standard form for part (a).The given standard form for part (a) is \(6x - 8y = 24\). This does not match the equation we derived, which is \(8x + 12y = 24\). However, we can adjust our equation by finding a common factor for \(A\) and \(B\) that would make the equation equivalent to the given one.Step 6: Adjust the equation to match the given form.We can divide our equation by 4 to simplify it:\[\frac{8x + 12y}{4} = \frac{24}{4}\]\[2x + 3y = 6\]This is a simplified form, but it does not match the given equation \(6x - 8y = 24\). It seems there might be a mistake in the given standard form for part (a) because it does not correspond to the graph described by the points (0,2) and (3,0).For part (b), we will use the correct standard form we derived:\[8x + 12y = 24\]The value for \(A\) is 8, and the value for \(B\) is 12.Final Answer:b. For the graph in part (b), the value for \(A\) is 8, and the value for \(B\) is 12.