Q15. - Algebra 2

Question

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

$\mathbf{2}\mathbf{x}-\mathbf{4}\mathbf{y}=\mathbf{10}$

Step-by-Step Solution

Answer

The slope of the given line is $\frac{1}{2}$ and the y-intercept of the given line is $-\frac{5}{2}$.

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 $2x-4y=10$.

Step 3 – Identify the slope and intercept

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

 

$2x-4y=10$  (Given equation)

 

$2x-4y-2x=10-2x$  (Subtract $2x$ from both sides)

 

$-4y=10-2x$  (Simplify)

 

$\frac{-4y}{-4}=\frac{10-2x}{-4}$  (Divide both sides by -4)

 

$y=\frac{1}{2}x-\frac{5}{2}$  (Simplify)

 

So, the given equation in slope-intercept form is $y=\frac{1}{2}x-\frac{5}{2}$.

 

Comparing the obtained equation, $y=\frac{1}{2}x-\frac{5}{2}$ with $y=mx+c$, $m=\frac{1}{2}$ and $c=-\frac{5}{2}$.

 

This implies that the slope of the given line is $\frac{1}{2}$ and the y-intercept of the given line is $-\frac{5}{2}$.