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

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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yagombyeR

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 $$\displaystyle{y}={0.6}{x}+{7}$$.