How to Find X-Intercept, Y-Intercept and Intersections

The y-intercept is the constant term in the equation $y=mx+c$. In this case, the y-intercept is 2, and it is the value of $y$ when $x=0$.

The x-intercept is found by setting $y=0$ and solving for $x$. $0=-4x+8$. Adding $4x$ to both sides gives $4x=8$. Dividing both sides by 4 gives $x=2$.

To find the intersection, set both equations equal to each other: $3x+2=-x+6$. Then solve for $x$: $3x+x=6-2\to 4x=4\to x=1$. Now substitute $x=1$ into either equation to find $y$: $y=3(1)+2=5$. So, the intersection point is $(1,5)$.

Set both equations equal to each other: $4x-1=-2x+5$. Then solve for $x$: $4x+2x=5+1\to 6x=6\to x=1$. Substitute $x=1$ into either equation to find $y$: $y=4(1)-1=3$. So, the intersection point is $(1,3)$.

Set both equations equal to each other: $2x+1=-x+10$. Then solve for $x$: $2x+x=10-1\to 3x=9\to x=3$. Now substitute $x=3$ into either equation to find $y$: $y=2(3)+1=7$. So, the intersection point is $(3,7)$.

Form the equation for the remaining fuel: $y=120-6x$, where $x$ is the number of hours. Since 60 litres are left, set $y=60$ and solve for $x$: $60=120-6x$. Then $6x=60\to x=10$. So, the car has been driven for 10 hours.