Question

Write the equation of the line that passes through the points (12, 4) and (22,9).

Answer 1

Given the following points that pass through the line:

Point A : 12,4

Point B : 22,9

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

`\text{ m = }(y_2-y_1)/(x_2-x_1)`
`\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}`
`\text{ m = }(5)/(10)\text{ = }(1)/(2)`

Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.

`\text{ y = mx + b}`
`\text{ 4 = (}(1)/(2))(12)\text{ + b }\rightarrow\text{ 4 = }(12)/(2)\text{ + b}`
`\text{ 4 = 6 + b}`
`4\text{ - 6 = b}`
`\text{ -2 = b}`

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

`\text{ y = mx + b}`
`\text{ y = (}(1)/(2))x\text{ + (-2)}`
`\text{ y = }(1)/(2)x\text{ - 2}`

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