Makahanap ng mga solusyon at sagot sa lahat ng iyong katanungan sa IDNStudy.com. Ang aming komunidad ay handang magbigay ng malalim at maaasahang mga sagot, anuman ang kahirapan ng iyong mga katanungan.

Find the slope-intercept form of the equation of the line passing through the points. Sketch the points

1.)  (4,3) (-4,-4)
2.) ( 3/4 , 3,2)  (-4/3 , 7/4)


Sagot :

[tex]1.) \\ (4,3), \ \ \ (-4,-4)\\\\First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} } \\ \\m=\frac{-4-3}{-4-4} = \frac{-7}{-8}=\frac{ 7}{ 8} \\ \\ Use \ point \ form \ of \ a \ line\ with \ one \ point:[/tex]

[tex]y-y_{1} =m(x-x _{1}) \\ \\y-3=\frac{7}{8} (x-4)\\\\y=\frac{7}{8}x-\frac{7}{2}+3\\\\y=\frac{7}{8}x-3.5+3\\\\y=\frac{7}{8}x-0.5[/tex]


[tex]2.)\\\\ ( \frac{3}{4} , 3.2)=( \frac{3}{4} , \frac{32}{10})=( \frac{3}{4} , \frac{16}{5}) , \\ (-\frac{4}{3} , \frac{7}{4} )\\\\First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]

[tex]m=\frac{ \frac{7}{4}-\frac{16}{5}}{-\frac{4}{3}-\frac{3}{4} } = \frac{ \frac{35}{20}-\frac{64}{20}}{-\frac{16}{12}-\frac{9}{12} } =\frac{-\frac{29}{20}}{-\frac{25}{12}} =(-\frac{29}{20}):(-\frac{25}{12} )=(-\frac{29}{20})*(-\frac{12} {25} )= \frac{87}{125} \\ \\ Use \ point \ form \ of \ a \ line\ with \ one \ point: \\\\ y-y_{1} =m(x-x _{1}) \\ \\y- \frac{16}{5}=\frac{87}{125} (x-\frac{3}{4} )[/tex]

[tex]y- \frac{16}{5}=\frac{87}{125} x-\frac{87}{125} \cdot \frac{3}{4} \\\\ y =\frac{87}{125} x-\frac{261}{500} +\frac{16}{5}\\\\y=\frac{87}{125} x-\frac{261}{500} +\frac{1600}{500}\\\\y=\frac{87}{125} x +\frac{1339}{500}[/tex]
 

View image Riza1
View image Riza1