What would be the linear equation for this function, & the graph? (X_1,Y_1)=(4,8), (X_2,Y_2)=(6,-9)

What would be the linear equation for this function, & the graph? (X_1,Y_1)=(4,8), (X_2,Y_2)=(6,-9)

Question
Linear equations and graphs
asked 2020-10-23
What would be the linear equation for this function, & the graph?
\(\displaystyle{\left({X}_{{1}},{Y}_{{1}}\right)}={\left({4},{8}\right)},{\left({X}_{{2}},{Y}_{{2}}\right)}={\left({6},-{9}\right)}\)

Answers (1)

2020-10-24
Formula used:
Point-slope form of line:
\(\displaystyle{\left({y}_{{2}}-{y}_{{1}}\right)}={m}{\left({x}_{{2}}-{x}_{{1}}\right)}\)
So, by the Point-Slope form of line the equation of line is given below:
\(\displaystyle{\left(-{9}-{8}\right)}={m}{\left({6}-{4}\right)}\)
\(\displaystyle-{17}={m}\times{2}\)
\(\displaystyle{2}{m}=-{17}\)
\(\displaystyle{m}=-\frac{{17}}{{2}}\)
Now \(\displaystyle{m}=-\frac{{17}}{{2}}\) and take any points to find the linear equation.
\(\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}={\left({4},{8}\right)}{\quad\text{and}\quad}{m}=-\frac{{17}}{{2}}\)
\(\displaystyle{\left({y}-{y}_{{1}}\right)}={m}{\left({x}-{x}_{{1}}\right)}\)
\(\displaystyle{\left({y}-{8}\right)}=-\frac{{17}}{{2}}{\left({x}-{4}\right)}\)
\(\displaystyle{\left({y}-{8}\right)}=\frac{{-{17}{x}}}{{2}}+{34}\)
\(\displaystyle{y}=\frac{{-{17}{x}}}{{2}}+{34}+{8}\)
\(\displaystyle{y}=\frac{{-{17}{x}}}{{2}}+{42}\)
\(\displaystyle{y}=\frac{{-{17}{x}+{84}}}{{2}}\)
\(\displaystyle{2}{y}=-{17}{x}_{{84}}\)
So, the graph is given below:
image
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