Algebra and Graphs

How to Find x Intercept, y Intercept, and Intersections

Solving Equations with 2 Variables

Simultaneous Equations

Solving Simultaneous Equations Graphically

Simultaneous Equations: Equal Values and Substitution Method

Elimination Method for Solving Simultaneous Equations

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How to Find x Intercept, y Intercept, and Intersections

Algebra and Graphs How to Find x Intercept, y Intercept, and Intersections

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🎬 Video Tutorial

(0:28) What is the y-Intercept? The y intercept is the point where a line crosses the y-axis. To find the y-intercept, substitute $x = 0$ into the equation. For example, in $y = 200 – 50x$, setting $x = 0$ gives $y = 200$, meaning the y-intercept is at (0, 200).
(0:55) What is the x-Intercept? The x intercept is the point where a line crosses the x-axis. To find the x-intercept, substitute $y = 0$ and solve for $x$. For example, in $y = 200 – 50x$, setting $y = 0$ gives $0 = 200 – 50x$, solving for $x$ results in $x = 4$, meaning the x-intercept is at (4, 0).
(1:52) How to Find the Intersection of Two Lines? The intersection of two lines is the point where they meet. To find this point, set the equations equal to each other and solve for $x$. Then, substitute $x$ back into one of the equations to find $y$.
(2:10) Finding Intersection (Example): Given $y = 200 – 50x$ and $y = 150 – 30x$, setting them equal gives $200 – 50x = 150 – 30x$, solving for $x$ gives $x = 2.5$, and substituting into $y = 150 – 30x$ gives $y = 75$, so the intersection is (2.5, 75).

📂 Revision Cards

Diagram explaining the x- and y-intercepts of linear equations using the equation y = 200 - 50x, illustrating where the line crosses the axes. — 1) x Intercept and y Intercept

Intersection of two linear equations, y = 200 - 50x and y = 150 - 30x, at point (2.5, 75) with x-axis as hours drove and y-axis as remaining distance. — 2) Intersection of Linear Equations

Steps to find the intersection of two linear equations by setting equations equal and solving for x and y, with equations and example values. — 3) How to Find the Intersection

🍪 Quiz Time - Practice Now!

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y-Intercepts and x-intercepts of Linear Equations

1 / 6

Q: In the equation $y = 3x + 2$, what is the y-intercept?

0

2

3

-3

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: Well done! 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 $x = 0$.

2 / 6

Q: In the equation $y = -4x + 8$, what is the x-intercept?

0

-2

2

4

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: Well done! 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 $x = 2$.

3 / 6

Q: Given the equations $y = 3x + 2$ and $y = -x + 6$, what is the intersection point?

(3, 5)

(1, 5)

(2, 4)

(4, 4)

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: Well done! 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).

4 / 6

Q: Find the point of intersection of the lines $y = 4x - 1$ and $y = -2x + 5$.

(4, 13)

(3, 9)

(1, 3)

(2, 7)

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: Well done! 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).

5 / 6

Q: Find the intersection of the lines $y = 2x + 1$ and $y = -x + 10$.

(3, 5)

(4, 2)

(5, 1)

(3, 7)

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: Well done! 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).

6 / 6

Q: A car starts with 120 liters of fuel. The car burns 6 liters of fuel every hour. After a few hours, 60 liters of fuel are left. Find out how many hours the car has been driven.

10 hours

8 hours

5 hours

12 hours

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.

Feedback: Well done! 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.

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