Question

Which is the equation for bc?

Answer 1

y=-4/5x+1 is the equation for bc

Answer 2

`y(x)=- (4)/(5)x+1=-0.8 x+1`

Explanation:

A line can be expressed using a slope-intercept form:

`y(x)=mx+b`

Where:

`m=Slope=(\Delta y)/(\Delta x) =(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=(1-5)/(0-(-5))= (-4)/(5) =-0.8`

Now, we have everything we need to find the equation for BC:

`y-5=-(4)/(5) (x-(-5))\\\\y-5=-(4)/(5) x-4\\\\y=-(4)/(5)+1=-0.8x+1`

Therefore, the equation for BC is:

`y(x)=- (4)/(5)x+1=-0.8 x+1`