[tex]\color{lime}\underline\mathbb{QUESTION:}[/tex]
Find the equation of the line that passes through the points (4,7) and (-2,6)
[tex]\\[/tex]
Slope-intercept form: y = mx + b
Representation:
- Let [tex]\sf{(x_1,y_1)=(4,7)\:and\:(x_2,y_2)=(-2,6)}[/tex]
================================
- [tex]\implies \sf{m=\frac{y_2-y_1}{x_2-x_1} }[/tex]
- [tex]\implies \sf{m=\frac{6-7}{-2-4} }[/tex]
- [tex]\implies \sf{m=\frac{1}{6} }[/tex]
---------------------------------
Finding b using any of the given points.
Using (4, 7)
- [tex]\implies \sf{y=\frac{1}{6} x+b }[/tex]
- [tex]\implies \sf{7=\frac{1}{6}(4)+b }[/tex]
- [tex]\implies \sf{7=\frac{2}{3}+b }[/tex]
- [tex]\implies \sf{7-\frac{2}{3}=b }[/tex]
- [tex]\implies \sf{\frac{19}{3}=b }[/tex]
In conclusion, 19/3 is the value of b.
[tex]\\[/tex]
[tex]\color{yellow}\underline\mathbb{ANSWER:}[/tex]
- The equation of the line is [tex]\sf{y = \frac{1}{6} x+\frac{19}{3} }[/tex].
