2.7

Straight line graphs

9 flashcards to master Straight line graphs

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Definition Flip

What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line?

Answer Flip

'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.

Definition Flip

What does the value 'c' represent in the equation y = mx + c?

Answer Flip

'c' represents the y-intercept, the point where the line crosses the y-axis. It's the value of y when x = 0.

Example: in y = 2x + 3, the line crosses the y-axis at y = 3.
Key Concept Flip

Determine the gradient of a line passing through the points (1, 5) and (3, 9).

Answer Flip

The gradient (m) is calculated as (change in y) / (change in x). So, m = (9-5) / (3-1) = 4 / 2 = 2. The gradient of the line is 2.

Key Concept Flip

Write the equation of a line with a gradient of -3 that passes through the point (0, 2).

Answer Flip

Since the line passes through (0,2), the y-intercept (c) is 2. Using y = mx + c, the equation of the line is y = -3x + 2.

Key Concept Flip

What is the relationship between the gradients of two parallel lines?

Answer Flip

Parallel lines have the same gradient. If line 1 has a gradient of m1 and line 2 has a gradient of m2, then for parallel lines, m1 = m2.

Key Concept Flip

What is the relationship between the gradients of two perpendicular lines?

Answer Flip

Perpendicular lines have gradients that are negative reciprocals of each other. If line 1 has a gradient of m1 and line 2 has a gradient of m2, then for perpendicular lines, m1 * m2 = -1.

Key Concept Flip

Find the midpoint of the line segment joining the points A(2, 4) and B(6, 8).

Answer Flip

The midpoint is found by averaging the x-coordinates and averaging the y-coordinates. Midpoint = ((2+6)/2, (4+8)/2) = (4, 6).

Key Concept Flip

Calculate the distance between the points (1, 2) and (4, 6). Give your answer to 2 decimal places.

Answer Flip

Use the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). Distance = sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.00.

Key Concept Flip

A line has the equation 2y + 4x = 8. What is its gradient?

Answer Flip

Rearrange the equation to the form y = mx + c. 2y = -4x + 8, so y = -2x + 4. The gradient, m, is -2.

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2.6 Graphs of functions 2.8 Functions

Key Questions: Straight line graphs

What does the value 'm' represent in the equation y = mx + c, and how does it affect the graph of the line?

'm' represents the gradient (slope) of the line. A larger positive 'm' indicates a steeper upward slope, while a negative 'm' indicates a downward slope. If m = 0, the line is horizontal.

What does the value 'c' represent in the equation y = mx + c?

'c' represents the y-intercept, the point where the line crosses the y-axis. It's the value of y when x = 0.

Example: in y = 2x + 3, the line crosses the y-axis at y = 3.

About Straight line graphs (2.7)

These 9 flashcards cover everything you need to know about Straight line graphs for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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