Question

A linear function is shown.

y-6=3/2(x-10)












Rewrite the function in standard form, Ax+By=C.

What is the value of C/A and what key feature does it represent?

Answer 1

To rewrite the given linear function \( y - 6 = \frac{3}{2}(x - 10) \) in standard form, \( Ax + By = C \), we will first distribute the \( \frac{3}{2} \) and then rearrange the equation.

1. Start by expanding the equation:
\[
y - 6 = \frac{3}{2}x - \frac{3}{2} \cdot 10
\]
\[
y - 6 = \frac{3}{2}x - 15
\]

2. Add 6 to both sides:
\[
y = \frac{3}{2}x - 15 + 6
\]
\[
y = \frac{3}{2}x - 9
\]

3. Rearrange the equation to get it in the form \( Ax + By = C \):
\[
-\frac{3}{2}x + y = -9
\]

4. To eliminate the fraction, multiply the entire equation by 2:
\[
-3x + 2y = -18
\]

Now the equation is in standard form, which is \( 3x - 2y = 18 \).

Here, we can identify \( A = 3 \), \( B = -2 \), and \( C = 18 \).

Next, we find \( \frac{C}{A} \):
\[
\frac{C}{A} = \frac{18}{3} = 6
\]

### Key Feature:
The value \( \frac{C}{A} \) represents the x-intercept of the line in standard form. In this case, it tells us that the line crosses the x-axis at the point where \( y = 0 \) when solving for \( x \) in the equation \( 3x - 2(0) = 18 \), leading to \( x = 6 \). Thus, the x-intercept is \( (6, 0) \).