Question

# Determine the equation of the line that passes through

Hint:

### We are given two points and we need to find the equation of the line passing through them. The equation of a line passing through two points (a, b) and (c, d) is

## The correct answer is: 8x - y + 18 = 0

### Step by step solution:

Let the given points be denoted by

(a, b) = (-3, -6)

(c, d) = (2, 34)

The equation of a line passing through two points and is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

5(y - 34) = 40(x - 2)

Expanding the factors, we have

5y - 170 = 40 x -80

Taking all the terms in the left hand side, we have

-40x + 5y - 170 + 80 = 0

Finally, the equation of the line is

-40x + 5y - 90=0

Dividing the equation throughout by(- 5), we get

This is the required equation.

.

The equation of a line passing through two points and is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

Expanding the factors, we have

Taking all the terms in the left hand side, we have

Finally, the equation of the line is

Dividing the equation throughout by(- 5), we get

This is the required equation.

.

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by a + by + c=0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc

### Related Questions to study

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive even numbers is 1 less than a perfect square

### Is the given conjecture correct? Provide arguments to support your answer.

The product of any two consecutive even numbers is 1 less than a perfect square

### Identify a linear polynomial.

### Identify a linear polynomial.

### Find the value of x. Identify the theorem used to find the answer.

### Find the value of x. Identify the theorem used to find the answer.

### identify a cubic polynomial.

### identify a cubic polynomial.

### Find the value of 𝑚 & 𝑛 to make a true statement.

(𝑚𝑥 + 𝑛𝑦)^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

### Find the value of 𝑚 & 𝑛 to make a true statement.

(𝑚𝑥 + 𝑛𝑦)^{2} = 4𝑥^{2} + 12𝑥𝑦 + 9𝑦^{2}

### 37. In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

i)Which equation models the scoring in the final round and the outcome of the contest

**Different Types of Variables**

### 37. In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

i)Which equation models the scoring in the final round and the outcome of the contest

**Different Types of Variables**