Respuesta :
Answer:
8. [tex]y=-\frac{7}{3}(x-1)+5[/tex]
9. [tex]y=\frac{4}{7}(x-2)-1[/tex]
10. [tex]y=-\frac{3}{4}x+3[/tex]
Step-by-step explanation:
The equation of a line passing through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given as:
[tex]y-y_{1}=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}})(x-x_{1})[/tex]
For #8:
[tex](x_{1},y_{1})[/tex] is [tex](1,5)[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](4, -2)[/tex].
Now, plug in these values and find the equation of the line. This gives,
[tex]y-5=(\frac{-2-5}{4-1})(x-1)\\y-5=(\frac{-7}{3})(x-1)\\y=-\frac{7}{3}(x-1)+5[/tex]
Therefore, the equation of a line passing through [tex](1,5)[/tex] and [tex](4, -2)[/tex] is [tex]y=-\frac{7}{3}(x-1)+5[/tex].
For #9:
[tex](x_{1},y_{1})[/tex] is [tex](2,-1)[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](-5, -5)[/tex].
Now, plug in these values and find the equation of the line. This gives,
[tex]y-(-1)=(\frac{-5-(-1)}{-5-2})(x-2)\\y+1=\frac{-5+1}{-7}(x-2)\\y+1=(\frac{-4}{-7})(x-2)\\y=\frac{4}{7}(x-2)-1[/tex]
Therefore, the equation of a line passing through [tex](2,-1)[/tex] and [tex](-5, -5)[/tex] is [tex]y=\frac{4}{7}(x-2)-1[/tex].
For #10:
[tex](x_{1},y_{1})[/tex] is [tex](0,3)[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](4, 0)[/tex].
Now, plug in these values and find the equation of the line. This gives,
[tex]y-3=(\frac{0-3}{4-0})(x-0)\\y-3=(\frac{-3}{4})(x)\\y=-\frac{3}{4}x+3[/tex]
Therefore, the equation of a line passing through [tex](0,3)[/tex] and [tex](4, 0)[/tex] is [tex]y=-\frac{3}{4}x+3[/tex].
