Answer:
Step-by-step explanation:
We are given coordinates of the line passed through (–5, –1) and (10, –7) .
Applying slope formula,
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:-7\right)[/tex]
Therefore,
[tex]m=\frac{-7-\left(-1\right)}{10-\left(-5\right)}[/tex]
[tex]m=-\frac{2}{5}[/tex]
Therefore, slope is [tex]m=-\frac{2}{5}[/tex].
Applying point-slope form [tex]y-y_1=m(x-x_1),[/tex] we get
[tex]y+7 = -\frac{2}{5}(x-10)[/tex]
[tex]y+7=-\frac{2}{5}(x-10)[/tex]
On multiplying both sides by 5, we get
[tex]5(y+7)=5\times-\frac{2}{5}(x+1)[/tex]
5y+35=-2(x-10)
5y+35=-2x+20
Adding 2x on both sides, we get
5y+25+2x=-2x+20+2x
2x+5y+35=20
Subtracting 35 from both sides, we get
2x+5y+35-35=20-35
2x+5y=-15.
Therefore, required equation is :
