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