How to Find x Intercept, y Intercept, and Intersections

Feedback: Not quite! 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 $x = 0$.

Feedback: Not quite! The x-intercept is found by setting $y = 0$ and solving for $x$. $0 = -4x + 8$. Adding $4x$ to both sides: $4x = 8$. Solving for $x$ by dividing both sides by 4: $x = 2$. So, the x-intercept is at $x = 2$.

Feedback: Not quite! To find the intersection, set both equations equal to each other: $3x + 2 = -x + 6$. Then, solve for $x$: $3x + x = 6 - 2 \rightarrow 4x = 4 \rightarrow x = 1$. Now, substitute $x = 1$ into either equation to find $y$: $y = 3(1) + 2 = 5$. So, the intersection point is (1, 5).

Feedback: Not quite! To find the intersection, set both equations equal to each other: $4x - 1 = -2x + 5$. Then, solve for $x$: $4x + 2x = 5 + 1 \rightarrow 6x = 6 \rightarrow x = 1$. Now substitute $x = 1$ into either equation to find $y$: $y = 4(1) - 1 = 3$. So, the intersection is at (1, 3).

Feedback: Not quite! To find the intersection, set both equations equal to each other: $2x + 1 = -x + 10$. Then, solve for $x$: $2x + x = 10 - 1 \rightarrow 3x = 9 \rightarrow x = 3$. Now substitute $x = 3$ into either equation to find $y$: $y = 2(3) + 1 = 7$. So, the intersection point is (3, 7).

Feedback: Not quite! To solve this, form the equation for the remaining fuel: $y = 120 - 6x$ where $x$ is the number of hours, and $y$ is the remaining fuel. We are given that 60 liters are left, so set $y = 60$ and solve for $x$: $60 = 120 - 6x \rightarrow 6x = 60 \rightarrow x = 10$. So, after 10 hours, there are 60 liters of fuel left.