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Consider the line with equation $2x+4.3y=\frac{1000}{99}\text{.}$

What is its $x$ -intercept?

What is its $y$ -intercept?

What is its slope?

Solution

To find the $x$ -intercept:
$\begin{aligned} 2x+4.3y\amp=\frac{1000}{99}\\ 2x+4.3(\substitute{0})\amp=\frac{1000}{99}\\ 2x\amp=\frac{1000}{99}\\ x\amp=\frac{500}{99} \end{aligned}$
So the $x$ -intercept is at $\left(\frac{500}{99},0\right)\text{.}$

To find the $y$ -intercept:
$\begin{aligned} 2x+4.3y\amp=\frac{1000}{99}\\ 2(\substitute{0})+4.3y\amp=\frac{1000}{99}\\ 4.3y\amp=\frac{1000}{99}\\ y\amp=\multiplyleft{\frac{1}{4.3}}\frac{1000}{99}\\ y\amp\approx2.349\ldots \end{aligned}$
So the $y$ -intercept is at about $(0,2.349)\text{.}$

Since we have the $x$ - and $y$ -intercepts, we can calculate the slope:
$m\approx-\frac{2.349}{\frac{500}{99}}=-\frac{2.349\cdot99}{500}\approx-0.4561\text{.}$

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