Q5. - Algebra 2

Question

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

$\mathbf{3}\mathbf{x}+\mathbf{2}\mathbf{y}-\mathbf{10}=\mathbf{0}$

Step-by-Step Solution

Answer

The slope of the given line is $-\frac{3}{2}$ and the y-intercept of the given line is 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.

Step 2 – List the given data

The given equation of the line is $3x+2y-10=0$.

Step 3 – Identify the slope and intercept

$3x+2y-10=0$  (Given equation)

$3x+2y-10-2y=0-2y$  (Subtract $2y$ from both sides)

$3x-10=-2y$  (Simplify)

$-2y=3x-10$  (Rearrange)

$\frac{-2y}{-2}=\frac{3x-10}{-2}$  (Divide both sides by -2)

$y=-\frac{3}{2}x+5$  (Simplify) 

So, the given equation in slope-intercept form is $y=-\frac{3}{2}x+5$. 

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

This implies that the slope of the given line is $-\frac{3}{2}$ and the y-intercept of the given line is 5.