Question

The line that contains the points (1,5) and (-3, 3). What is the equation of the line?

Answer 1

Given the following points that pass through a line:

Let,

Point A : (-3, 3)

Point B : (1, 5)

Let's determine the equation of the line in Slope-Intercept Form: y = mx + b

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

`\text{ m = }(y_2-y_1)/(x_2-x_1)`
`=\text{ }\frac{5\text{ - 3}}{1\text{ - (-3)}}\text{ = }\frac{5\text{ - 3}}{1\text{ + 3}}`
`m\text{ = }(2)/(4)\text{ = }(1)/(2)`

Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 1,5 in y = mx + b.

`\text{ y = mx + b}`
`\text{ 5 = (}(1)/(2))(1)\text{ + b}`
`5\text{ - }(1)/(2)\text{ = b}`
`(10)/(2)\text{ -}\frac{1}{2\text{ }}\text{ = b}`
`\text{ }(9)/(2)\text{ = b}`

Step 3: Let's complete the equation. Substitute m = 1/2 and b = 9/2 in y = mx + b.

`\text{ y = (}(1)/(2))x\text{ + (}(9)/(2))`
`\text{ y = }(1)/(2)x\text{ + }(9)/(2)`

Therefore, the equation of the line is y = 1/2x + 9/2.