To rewrite the given equation [tex]\( 14x - 7y = 42 \)[/tex] in slope-intercept form, we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. The slope-intercept form of a linear equation is given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Let's follow these steps to achieve the desired form:
1. Start by isolating the term containing [tex]\( y \)[/tex]. We will do this by subtracting [tex]\( 14x \)[/tex] from both sides of the equation:
[tex]\[
14x - 7y - 14x = 42 - 14x
\][/tex]
Simplifying this, we get:
[tex]\[
-7y = -14x + 42
\][/tex]
2. Next, to solve for [tex]\( y \)[/tex], we need to divide every term in the equation by [tex]\(-7\)[/tex]:
[tex]\[
\frac{-7y}{-7} = \frac{-14x}{-7} + \frac{42}{-7}
\][/tex]
This simplifies to:
[tex]\[
y = 2x - 6
\][/tex]
Now the equation is in slope-intercept form [tex]\( y = mx + b \)[/tex].
From this form, we can identify:
- The slope [tex]\( m \)[/tex]:
[tex]\[
m = 2
\][/tex]
- The y-intercept [tex]\( b \)[/tex]:
[tex]\[
b = -6
\][/tex]
So, the equation in slope-intercept form is:
[tex]\[ y = 2x - 6 \][/tex]
Thus, the slope of the line is:
[tex]\[ m = 2 \][/tex]
The y-intercept of the line is:
[tex]\[ b = -6 \][/tex]
