Kaeden Hoffman

2022-07-06

With this information I am to find the linear equation: f(−5)=−4 and f(5)=2
The solution is provided as $y=\frac{3}{5}x-1$ however I arrived at $y=\frac{7}{10}x-\frac{3}{2}$
Here is my working:
Using these points, find the equation: (-5,-4)(5, 2)
the slope m: $m=\frac{y1-y}{x1-x}$=$\frac{2+5}{5+5}$=$\frac{7}{10}$
Now that I have m, plug the values of one of the pairs into the linear function form to find b: $y=mx+b$
$2=\frac{7}{10}\left(5\right)+b$
$\frac{7}{10}\left(5\right)+b=2$
$\frac{7}{2}+b=2$ #7/10 * 5 = 7/2
$b=2-\frac{7}{2}$
$b=-\frac{3}{2}$
$y=\frac{7}{10}x+\frac{3}{2}$
Where did I go wrong and how can I arrive at $y=\frac{3}{5}x-1$?

amanhantmk

Expert

Probably you made a mistake in the step below:
“Using these points, find the equation: (-5,-4)(5, 2)”
You should calculate 2-(-4)

therightwomanwf

Expert

Point-slope form for the line might be a bit easier:
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}=\frac{2-\left(-4\right)}{5-\left(-5\right)}=\frac{3}{5}$
$y-2=\frac{3}{5}\left(x-5\right)$
$y=\frac{3}{5}x-1$

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