Question

Two points on a graph (1,2) (4,1). find the equation that represents the linear function

Answer 1

Let's make an equation that represents the linear function passing through points (1,2) and (4,1) by Slope-Intercept Form.

`\text{ y = mx+b}`

In making an equation in this form, we must first determine the value of the slope (m) and the y-intercept (b) of the line.

For determining the value of the slope, we use this formula,

`\text{ m = }\frac{y_2-y_1\text{ }}{x_2-x_1}`

Let's substitute (x1,y1) = (1,2) and (x2,y2) = (4,1), we get,

`\text{ m = }\frac{1\text{ - 2}}{4\text{ -1}}\text{ = }(-1)/(3)\text{ = -}(1)/(3)`

Let's now compute for the value of the y-intercept (b),

m = -1/3 and (x1,y1) = (1,2)

`\text{ y = mx + b}`
`\text{ (2) = (-}(1)/(3))(1)\text{ + b}`
`\text{ 2 = -}(1)/(3)\text{ + b }\rightarrow\text{ b = 2 + }(1)/(3)\text{ = }\frac{6\text{ + 1}}{3}`
`\text{ b = }(7)/(3)`

Let's now make the equation substituting the value of m and b.

m = -1/3 and b = 7/3

`\text{ y = (}(-1)/(3))x\text{ + }(7)/(3)`
`\text{ y = -}(1)/(3)x\text{ + }(7)/(3)`