## 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?

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

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

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What is the condition for two lines to be perpendicular?

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How do you check if two lines are perpendicular?

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

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What is Euler's formula used for in polyhedral?

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

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What is the rise/run formula used to determine?

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

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

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

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

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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`

.

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