Using point-slope form: y - y1 = m(x - x1) => y - 3 = 2(x - 1) => y = 2x + 1.

Slope m = (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) => y = 2x + 1.

The slope of the given line is 3.\nThe slope of the perpendicular line is -1/3.\nUsing point-slope form: y - 5 = -1/3(x - 2) gives y = -1/3x + 7.

The slope of the perpendicular line is -1/2. Using point-slope form: y - 2 = -1/2(x - 1) => y = -1/2x + 5/2.

Using point-slope form: y - y1 = m(x - x1) => y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.

Using point-slope form: y - 3 = -1(x - 2) => y = -x + 5.

Using point-slope form: y - y1 = m(x - x1) => y - 3 = 4(x - 2) => y = 4x - 8 + 3 => y = 4x - 5.

First, find the slope: m = (3 - 2) / (2 - 1) = 1. Using point-slope form: y - 2 = 1(x - 1) => y = x + 1.

Slope = (4 - 2) / (3 - 1) = 1. Using point-slope form: y - 2 = 1(x - 1) => y = x + 1.

Calculate the slope: m = (y2 - y1)/(x2 - x1) = (6 - 2)/(3 - 1) = 2.\nUsing point-slope form: y - 2 = 2(x - 1) gives y = 2x.

First, factor out the common term 2x from 2x^2 + 8x. This gives us 2x(x + 4).

Factor out the common term 2: 2(x^2 - 4). Then factor x^2 - 4 as (x - 2)(x + 2). Thus, the final factorization is 2(x - 4)(x + 4).

The greatest common factor is 4x. Factoring it out gives us 4x(x - 3).

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).

To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factored form is (x - 2)(x - 3).

This is a perfect square trinomial. The factored form is (x - 3)(x - 3) or (x - 3)^2.

This is a difference of squares. The factored form is (x - 3)(x + 3).

Step 1: Factor out the common term: 2x(x + 4).

Step 1: Factor out the common term: 2(x^2 - 4). Step 2: Recognize the difference of squares: 2(x - 4)(x + 4).

First, factor out 3: 3(x^2 - 4). Then, factor the difference of squares: 3(x - 2)(x + 2).

Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor: (x + 2)(x + 3).

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor as (x + 5)(x + 2).

To factor, we look for two numbers that multiply to 24 and add to -10. The numbers -4 and -6 work, so the factored form is (x - 4)(x - 6).

This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).

This is a difference of squares: x^2 - 4 = (x - 2)(x + 2).

The polynomial x^2 - 6x + 9 can be factored as (x - 3)(x - 3) or (x - 3)^2.

Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).

This quadratic can be factored as (x + 3)(x + 3) or (x + 3)^2.

Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3. Step 2: Write the factors: (x - 2)(x - 3).

To factor, we look for two numbers that multiply to 10 and add to -7. The numbers -2 and -5 work, so the factored form is (x - 2)(x - 5).