Question

A linear function is shown.
(y-3)=4/5 (x-15)
Rewrite the function in slope-intercept form and standard form.

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Slope-intercept form [ ]
Standard form [ ]
choices:
y=4/5x-15, 4x-5y=45, 4x-5y=75, y=4/5x+9, 4x+5y=-45, y=4/5x-9, 4x+5y=75

Answer 1

To rewrite the given function \((y-3)=\frac{4}{5} (x-15)\) in slope-intercept form (y = mx + b) and standard form (Ax + By = C), we can start by simplifying the equation.

### Step 1: Convert to Slope-Intercept Form
1. Expand the right side:
\[
y - 3 = \frac{4}{5}x - \frac{4}{5} \cdot 15
\]
\[
y - 3 = \frac{4}{5}x - 12
\]
2. Add 3 to both sides:
\[
y = \frac{4}{5}x - 12 + 3
\]
\[
y = \frac{4}{5}x - 9
\]

So the slope-intercept form is:
**Slope-intercept form:** \(y = \frac{4}{5}x - 9\)

### Step 2: Convert to Standard Form
We need to rewrite \(y = \frac{4}{5}x - 9\) in the form \(Ax + By = C\):
1. Multiply through by 5 to eliminate the fraction:
\[
5y = 4x - 45
\]
2. Rearranging gives:
\[
-4x + 5y = -45
\]
3. Multiply through by -1 to get the standard form with a positive \(A\):
\[
4x - 5y = 45
\]

So the standard form is:
**Standard form:** \(4x - 5y = 45\)

### Final Responses
- Slope-intercept form: \(y = \frac{4}{5}x - 9\)
- Standard form: \(4x - 5y = 45\)

Now, we can fill in the input boxes with these answers.

Slope-intercept form [**y = \frac{4}{5}x - 9**]
Standard form [**4x - 5y = 45**]