Mathematics Formulas and Equations

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Questions and Answers

What happens to the line when x = -3?

The line will go vertically across the x-axis because there is no y-intercept.

What is the formula to calculate the midpoint of a line segment?

M = (x₁ + x₂)/2 , (y₁ + y₂)/2

How do you find the x-coordinate using the midpoint formula?

x = (x₁ + x₂)/2

What is the formula to calculate the length of a line segment?

√((y¹ - y²)² + (x¹ - x²)²) Signup and view all the answers

What is the method to find the intersection of two lines?

Equating the two equations, y = y. Signup and view all the answers

How do you find the x-coordinate of the intersection point?

Solve the equation obtained by equating the two lines. Signup and view all the answers

What is the condition for two lines to be perpendicular?

The product of their gradients equals -1. Signup and view all the answers

How do you check if two lines are perpendicular?

Multiply the gradients of the two lines. If the product equals -1, they are perpendicular. Signup and view all the answers

What is the formula to determine the equation of a line when given two points and the gradient?

y-y_1=m(x-x_1) Signup and view all the answers

What is Euler's formula used for in polyhedral?

E=F+V-2 Signup and view all the answers

How do you find the gradient of a line given two sets of coordinates?

m=(y^2-y^1)/(x^2-x^1) Signup and view all the answers

What is the rise/run formula used to determine?

The gradient (m) of a line Signup and view all the answers

What is the x and y intercept method used to find?

The x and y intercepts of a line Signup and view all the answers

How do you find the y-intercept of a line given the equation 2y=3x+6?

Let y=0 and solve for x, then let x=0 and solve for y Signup and view all the answers

What does the equation y=4 represent in terms of the graph of a line?

A horizontal line with a y-intercept of 4 Signup and view all the answers

What is the purpose of rearranging an equation to the form y=mx+c?

To find the gradient (m) and y-intercept (c) of a line Signup and view all the answers

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Study Notes

Equations of Lines

The point-slope form equation is y - y_1 = m(x - x_1), where m is the gradient and (x_1, y_1) is a point on the line.
The gradient can be calculated using m = (y_2 - y_1) / (x_2 - x_1).
The gradient-intercept form equation is y = mx + c, where m is the gradient and c is the y-intercept.

Euler's Formula

Euler's formula is E = F + V - 2, where E is the number of edges, F is the number of faces, and V is the number of vertices in a polyhedral.

Midpoint Formula

The midpoint formula is M = ((x_1 + x_2) / 2, (y_1 + y_2) / 2), where (x_1, y_1) and (x_2, y_2) are two points on a line segment.

Distance Formula

The distance formula is √((y_2 - y_1)^2 + (x_2 - x_1)^2), where (x_1, y_1) and (x_2, y_2) are two points.

Intersection of Lines

To find the intersection of two lines, set the two equations equal to each other, i.e., y = y.
Solve for x and then substitute the value of x into one of the original equations to find y.
The product of the gradients of two perpendicular lines is -1.