Question

Write an equation of the line that passes through a pair of points: 5 4 37 2 1+ 4 -3 -2 -1 1 -3 a. y = x + 3 b. y = x - 3 C. y = -x + 2 d. y = -x-2 Please select the best answer from the choicon

Answer 1

From the given, it shows two points that pass through the given graph. These points are:

Point A : x1, y1 = 4, 1

Point B : x2, y2 = 5, 2

We will be using these points in generating the equation of the line.

Step 1: Let's determine the slope m of the line.

`\text{ m = }(y_2-y_1)/(x_2-x_1)\text{ = }\frac{\text{ 2 - 1}}{\text{ 5 - 4}}\text{ = }(1)/(1)\text{ = 1}`

Step 2: Let's determine the y-intercept b. Substitute x,y = 4, 1 and m = 1 in y = mx + b.

`\text{ y = mx + b}`
`\text{ 1 = (1)(4) + b}`
`\text{ 1 = 4 + b}`
`\text{ 1 - 4 = b}`
`\text{ -3 = b}`

Step 3: Let's complete the equation. Substitute m = 1 and b = -3 in y = mx + b.

`\text{ y = mx + b}`
`\text{ y = (1)x + (-3)}`
`\text{ y = x - 3}`

Therefore, the equation of the line is y = x - 3.

The answer is letter B.