One way to find the formula of a line passing through (15,16) and (30,25) is by

York 2021-09-20 Answered

One way to find the formula of a line passing through (15,16) and (30,25) is by using a table, as shown below. Complete parts (a) and (b) below.
a) Complete the box in the first row.
\(\begin{array}{|c|c|} \hline x&y\\ \hline 0&\\ \hline 15&16\\ \hline 30&25\\ \hline \end{array}\)
b) Report the formula of the line in slope-intercept form.
\(y=\)___\(+x\)___

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Expert Answer

yagombyeR
Answered 2021-09-21 Author has 14235 answers

Step 1
line passing through point
\(\displaystyle{\left({15},{16}\right)}{\quad\text{and}\quad}{\left({30},{25}\right)}\)
The equation of line is given by
\(\displaystyle{\frac{{{x}-{15}}}{{{30}-{15}}}}={\frac{{{y}-{16}}}{{{25}-{16}}}}\)
\(\displaystyle{\frac{{{x}-{15}}}{{{15}}}}={\frac{{{y}-{16}}}{{{9}}}}\)
\(\displaystyle{x}-{15}={\frac{{{5}}}{{{3}}}}{y}-{16}\)
\(\displaystyle{3}{x}-{45}={5}{y}-{80}\)
\(\displaystyle{3}{x}+{35}={5}{y}\)
\(\displaystyle{y}={\frac{{{3}}}{{{5}}}}{x}+{7}\)
\(\displaystyle{y}={0.6}{x}+{7}\)
Step 2
a) Complete box.
\(\begin{array}{|c|c|} \hline x&y\\ \hline 0&7\\ \hline 15&16\\ \hline 30&25\\ \hline \end{array}\)
b) Report line in slope-intercept form \(\displaystyle{y}={0.6}{x}+{7}\).

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