Answer:
[tex]y(x)=- \frac{4}{5}x+1=-0.8 x+1[/tex]
Step-by-step explanation:
A line can be expressed using a slope-intercept form:
[tex]y(x)=mx+b[/tex]
Where:
[tex]m=Slope=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]b=y-axis\hspace{3}intercept[/tex]
Given a point on the line [tex]P(x_1,y_1)[/tex] it is possible to obtain the previous equation from the following formula:
[tex]y-y_1=m(x-x_1)[/tex]
From the graph we can extract the two points necessary to find the equation. As you can see:
[tex]B(x_1,y_1)=(-5,5)\\C(x_2,y_2)=(0,1)[/tex]
So, let's find the slope:
[tex]m=\frac{1-5}{0-(-5)}= \frac{-4}{5} =-0.8[/tex]
Now, we have everything we need to find the equation for BC:
[tex]y-5=-\frac{4}{5} (x-(-5))\\\\y-5=-\frac{4}{5} x-4\\\\y=-\frac{4}{5}+1=-0.8x+1[/tex]
Therefore, the equation for BC is:
[tex]y(x)=- \frac{4}{5}x+1=-0.8 x+1[/tex]
