Answer:
B) intercepts are [tex]x=-5.8\ and\ y =-9.7[/tex]
Step-by-step explanation:
Given coordinates are [tex](-4,-3)\ and\ (-1,-8)[/tex]
The intercepts are the points where the line meets with the x-axis and the y-axis.
The Y-intercept is where x-coordinate is zero.
And X-intercept is where y-coordinate is zero.
We will use the slope intercept form of equation of line to compute Y-intercept.
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is slope of line. And [tex]b[/tex] is Y-intercept.
We will find slope of line and plug in this equation to compute Y-intercept.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]x_1=-4,y_1=-3\ and\ x_2=-1,y_2=-8\\\\m=\frac{-8-(-3)}{-1-(-4)}\\m=\frac{-5}{3}[/tex]
[tex]Plug\ x=-4,y=-3\ in\ y=mx+b\\\\-3=\frac{-5}{3}\times-4+b\\\\-3=\frac{20}{3}+b\\\\-3=6.67+b\\-3-6.67=b\\\\b=-9.7[/tex]
[tex]y=\frac{-5}{3}x-9.7[/tex]
Now, plug [tex]y=0[/tex] in the equation [tex]y=mx+b[/tex] to find X-intercept.
[tex]0=\frac{-5}{3}x-9.7\\ \\9.7=\frac{-5}{3}x\\\\9.7\times3=-5x\\\\x=-9.7\frac{3}{5}\\ \\x=-5.8[/tex]
So, our intercepts are [tex]x=-5.8\ and\ y =-9.7[/tex]
