To rewrite the equation [tex]\(6x + 7y = 9\)[/tex] in slope-intercept form, we need to express it in the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
Let's start by isolating [tex]\(y\)[/tex] on one side of the equation.
1. Begin with the equation:
[tex]\[
6x + 7y = 9
\][/tex]
2. Subtract [tex]\(6x\)[/tex] from both sides to isolate the term with [tex]\(y\)[/tex]:
[tex]\[
7y = 9 - 6x
\][/tex]
3. Divide every term by 7 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{9}{7} - \frac{6x}{7}
\][/tex]
This simplifies to:
[tex]\[
y = -\frac{6}{7}x + \frac{9}{7}
\][/tex]
So, the equation in slope-intercept form is:
[tex]\[
y = -\frac{6}{7}x + \frac{9}{7}
\][/tex]
From this equation, we can identify the slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(b\)[/tex]).
- The slope [tex]\(m\)[/tex] is [tex]\( -\frac{6}{7} \)[/tex].
- The y-intercept [tex]\(b\)[/tex] is [tex]\( \frac{9}{7} \)[/tex].
Thus, the equation in slope-intercept form is:
[tex]\[
y = -\frac{6}{7}x + \frac{9}{7}
\][/tex]
The slope of the equation is:
[tex]\[
-\frac{6}{7}
\][/tex]
