Mathematics Formulas and Equations

16 Questions

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)

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

Equating the two equations, y = y.

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

Solve the equation obtained by equating the two lines.

What is the condition for two lines to be perpendicular?

The product of their gradients equals -1.

How do you check if two lines are perpendicular?

Multiply the gradients of the two lines. If the product equals -1, they are perpendicular.

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)

What is Euler's formula used for in polyhedral?

E=F+V-2

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

m=(y^2-y^1)/(x^2-x^1)

What is the rise/run formula used to determine?

The gradient (m) of a line

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

The x and y intercepts of a line

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

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

A horizontal line with a y-intercept of 4

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

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.

This quiz covers formulas and equations in mathematics, including the point-slope form and Euler's formula for polyhedral shapes.

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