Question

How do I find the value of k so that the line (2+k)x + (2-k)=15 has slope 3/2

Answer 1

The value of k must be:

$\boxed{k=\frac{2}{5}}$

Explanation:

$(2+k)x+(2-k)y=15$

First of all, you need to know that the Slope-intercept form of the equation of a line is given by:

$y=mx+b \\ \\ m:Slope \\ \\ b:y-intercept$

So, let's arrange our given equation:

$(2+k)x+(2-k)y=15 \\ \\ (2-k)y=-(2+k)x+15 \\ \\ y=\frac{2+k}{2-k}x+\frac{15}{2-k}$

As you can see, we can know that:

$m=\frac{2+k}{2-k} \\ \\ b=\frac{15}{2-k}$

But we know that the slope is 3/2:

$\frac{2+k}{2-k} =\frac{3}{2} \\ \\ Solving \ for k: \\ \\ 2(2+k)=3(2-k) \\ \\ 4+2k=6-3k \\ \\ 2k+3k=6-4 \\ \\ 5k=2 \\ \\ k=\frac{2}{5}$

Learn more:

Relationship among proportional relationships lines, rates of change, and slope:

https://brainly.com/question/674693

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