To determine the slope of the linear equation [tex]\( 20x + 16y = 3 \)[/tex], we need to transform it into the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
Here are the steps:
1. Start with the given equation:
[tex]\[
20x + 16y = 3
\][/tex]
2. Solve for [tex]\( y \)[/tex] by isolating it on one side of the equation. First, subtract [tex]\( 20x \)[/tex] from both sides to move the [tex]\( x \)[/tex]-term to the right side:
[tex]\[
16y = -20x + 3
\][/tex]
3. Next, divide both sides of the equation by 16 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \left(-\frac{20}{16}\right)x + \frac{3}{16}
\][/tex]
4. Simplify the fraction [tex]\(\frac{20}{16}\)[/tex]:
[tex]\[
y = \left(-\frac{5}{4}\right)x + \frac{3}{16}
\][/tex]
In the simplified form [tex]\( y = mx + b \)[/tex], the coefficient of [tex]\( x \)[/tex] is the slope [tex]\( m \)[/tex].
Thus, the slope [tex]\( m \)[/tex] of the equation [tex]\( 20x + 16y = 3 \)[/tex] is:
[tex]\[
m = -\frac{5}{4}
\][/tex]
So, the correct choice is:
A. The slope of [tex]\( 20x + 16y = 3 \)[/tex] is [tex]\( -\frac{5}{4} \)[/tex].
