To determine which line corresponds to the linear equation [tex]\(3y + 3x = 9\)[/tex], let's convert this equation into slope-intercept form [tex]\(y = mx + b\)[/tex].
Here’s the step-by-step process:
1. Start with the given equation:
[tex]\[
3y + 3x = 9
\][/tex]
2. Isolate [tex]\(y\)[/tex] on one side of the equation:
- Subtract [tex]\(3x\)[/tex] from both sides to get [tex]\(y\)[/tex] alone on one side.
[tex]\[
3y = -3x + 9
\][/tex]
3. Divide every term by 3 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = -x + 3
\][/tex]
Now, the linear equation is in the form [tex]\(y = -x + 3\)[/tex], which is the slope-intercept form.
By analyzing this form:
- The slope ([tex]\(m\)[/tex]) is -1.
- The y-intercept ([tex]\(b\)[/tex]) is 3.
Given these characteristics, the line that correctly matches this equation is the correct one.
Therefore, the answer to the question "Which line has the linear equation [tex]\(3y + 3x = 9\)[/tex]?" is:
Line A
