Q3. - Algebra 2

Question

3. Explain how to find the slope of a line parallel to the graph of $\mathbf{3}\mathbf{x}-\mathbf{5}\mathbf{y}=\mathbf{2}$.

Step-by-Step Solution

Answer

The slope of a line parallel to the graph of $3x-5y=2$ is $\frac{3}{5}$.

Step 1 – State the concept

The general equation of a straight line in slope-intercept form is given as $y=mx+c$, where $m$ is the slope and $c$ is the y-intercept.

 The slopes of parallel lines are equal.

Step 2 – List the given data

The given equation of the line is $3x-5y=2$.

Step 3 – Find the slope

$3x-5y=2$   (Given equation)

 $3x-5y-3x=2-3x$   (Subtract $3x$ from both sides)

$-5y=2-3x$   (Simplify)

$\frac{-5y}{-5}=\frac{2-3x}{-5}$  (Divide both sides by -5)

 $y=\frac{3}{5}x-\frac{2}{5}$  (Simplify)

 Comparing the given equation with $y=mx+c$, $m=\frac{3}{5}$ and $c=-\frac{2}{5}$

 This implies that the slope of the given line is$\frac{3}{5}$.

 Since a line parallel to this line will have the same slope, such a line will also have a slope of $\frac{3}{5}$.

So, the slope of a line parallel to the graph of the given equation is $\frac{3}{5}$.