Algebra and Graphs

Basic Expressions and Formulas

Introduction to Mappings

Introduction to Formulas

Expressions with One Variable

Equations and Simplifications

Simplifying Expressions

How to Solve an Equation

Solving Rational Equations

Simplifying Expressions with Multiple Variables

Expanding and Binomials

Expanding Double Brackets

Square of a Binomial

Quadratic Equations

Simple Quadratic Equations

Vertex Form and Parabola Transformations

Converting Quadratics: General and Vertex Form

Determining Quadratic Equations

Solving Simple Quadratic Equations

Factorization Method for Solving Quadratic Equations

Solving Quadratic Equations: Quadratic Formula

Functions and Graphs

Plotting and Reflecting Points on the Coordinate Grid

Introduction to Functions and Graphs

Gradient and Y-Intercept in Linear Equations

Finding the Equation of a Straight Line

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Previous Lesson

Gradient and Y-Intercept in Linear Equations

Algebra and Graphs Gradient and Y-Intercept in Linear Equations

🎬 Video Tutorial

(0:01) Linear equation basics: In $y = mx + c$, $m$ is the gradient (slope) and $c$ is the y-intercept. Understanding $m$ and $c$ is essential for graphing straight lines.
(0:24) Interpreting the gradient $m$: The gradient ($m$) shows how steep the line is. A positive $m$ means an upward slope, while a negative $m$ means a downward slope.
(2:55) Graphing Linear Equations: For $y = 2x + 1$, start at the y-intercept $(0,1)$, then move 1 step right and 2 steps up to plot the second point because $m$ is 2. Finally, create a straight line through these points.

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📂 Revision Cards

Linear equation y = mx + c showing the gradient (m) and y-intercept (c), with a graph of a straight line. — 1) m and c in Linear Equations

Linear equation y=mx+c with highlighted y-intercept c where line crosses y-axis. Diagram shows lines with different y-intercepts, one passing origin. — 2) Intercept Linear Equations

Graph illustrating y = mx + c with explanations of gradient (m) and y-intercept (c), and examples of positive and negative gradients. — 3) Slope of Linear Equations

How to draw a linear equation with gradient (m) and y-intercept (c) shown on a graph, step-by-step guide with illustrations. — 4) Draw a Linear Equation

Steps to draw a linear equation y = -3x + 4, find y-intercept at 4, move 1 step right and 3 steps down, and connect points with the line. — 5) Draw a Linear Equation

🍪 Quiz

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Gradient and Y-Intercept in Linear Equations

1 / 6

Q: What is the slope (m) of the line for the equation $y = -4x + 3$?

3

-4

4

3

Feedback: Not quite! The slope (m) is the number in front of the variable $x$, called the coefficient. In this case, -4 is the coefficient of $x$, so the correct answer is -4.

Feedback: Well done! The slope (m) is the number in front of the variable $x$, called the coefficient. In this case, -4 is the coefficient of $x$, so the correct answer is -4.

2 / 6

Q: What is the y-intercept (c) of the equation y = 5x - 7?

-5

5

7

-7

Feedback: Not quite! The y-intercept is the value of $y$ when $x = 0$. In the equation $y = 5x - 7$, when $x = 0$, $y = -7$.

Feedback: Well done! The y-intercept is the value of $y$ when $x = 0$. In the equation $y = 5x - 7$, when $x = 0$, $y = -7$.

3 / 6

Q: Based on the equation $y = x - 6$, what is the slope (m) of the line?

-1

1

6

-6

Feedback: Not quite! The slope (m) is the coefficient of $x$. In this equation, the coefficient of $x$ is 1, so the slope is 1.

Feedback: Well done! The slope (m) is the coefficient of $x$. In this equation, the coefficient of $x$ is 1, so the slope is 1.

4 / 6

Q: What is the equation of the line with slope $m = 4$ and y-intercept $c = -2$?

$y = -4x - 2$

$y = 4x + 2$

$y = 4x - 2$

$y = -4x + 2$

Feedback: Not quite! The equation of a straight line is written as $y = mx + c$, where m is the slope and c is the y-intercept. Here, the slope is 4 and the y-intercept is -2. So, the correct equation is $y = 4x - 2$.

Feedback: Well done! The equation of a straight line is written as $y = mx + c$, where m is the slope and c is the y-intercept. Here, the slope is 4 and the y-intercept is -2. So, the correct equation is $y = 4x - 2$.

5 / 6

Q: In the equation y = 3x - 4, if the slope (m) is doubled, what is the new equation of the line?

$y = -6x - 4$

$y = 6x - 4$

$y = 3x - 8$

$y = -3x - 8$

Feedback: Not quite! Doubling the slope means multiplying the original slope ($m = 3$) by 2. This gives a new slope of 6. The y-intercept ($c = -4$) stays the same, so the new equation becomes $y = 6x - 4$.

Feedback: Well done! Doubling the slope means multiplying the original slope ($m = 3$) by 2. This gives a new slope of 6. The y-intercept ($c = -4$) stays the same, so the new equation becomes $y = 6x - 4$.

6 / 6

Q: For the equation $y = 3x + 5$, what happens to $y$ if $x$ increases by 1?

decrease by 3

increase by 5

increase by 3

decrease by 5

Feedback: Not quite! The slope is the change in $y$ for each 1 unit change in $x$. In this equation, the slope is 3, meaning for every step to the right (increase of 1 in $x$), $y$ increases by 3.

Feedback: Well done! The slope is the change in $y$ for each 1 unit change in $x$. In this equation, the slope is 3, meaning for every step to the right (increase of 1 in $x$), $y$ increases by 3.

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