Q16. - Algebra 2

Question

State the slope and y-intercept of the graph of each equation.

$\mathbf{3}\mathbf{x}+\mathbf{5}\mathbf{y}-\mathbf{30}=\mathbf{0}$

Step-by-Step Solution

Answer

The slope of the given line is $-\frac{3}{5}$ and the y-intercept of the given line is 6.

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.

Step 2 – List the given data

The given equation of the line is $3x+5y-30=0$.

Step 3 – Identify the slope and intercept

Convert the given equation to slope-intercept form as follows:

 

$3x+5y-30=0$  (Given equation)

 

$3x+5y-30-5y=0-5y$  (Subtract $5y$ from both sides)

 

$3x-30=-5y$  (Simplify)

 

$-5y=3x-30$  (Rearrange)

 

$\frac{-5y}{-5}=\frac{3x-30}{-5}$ (Divide both sides by -5)

 

$y=-\frac{3}{5}x+6$  (Simplify)

 

So, the given equation in slope-intercept form is $y=-\frac{3}{5}x+6$.

 

Comparing the obtained equation, $y=-\frac{3}{5}x+6$ with $y=mx+c$, $m=-\frac{3}{5}$ and $c=6$.

 

This implies that the slope of the given line is $-\frac{3}{5}$ and the y-intercept of the given line is 6.