Question

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

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

Short answer

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

Step-by-step solution

– 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.

– List the given data

The given equation of the line is $2x-4y=10$.

– 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 $-\frac{5}{2}$.