Question

What is the point slope form of the equation for a line that passes through (6,-1) with a slope of 2.

Answer 1

`y+1=2(x-6)`

Explanation:

The slope of the line is 2. Hence, m = 2

And it passes through the point (6,-1). Hence,
`x_1=6,y_1=-1`

The point slope form of the line is given by the equation

`y-y_1=m(x-x_1)`

Substituting the known values, we get

`y-(-1)=2(x-6)`

On simplifying, we get

`y+1=2(x-6)`

Therefore, the point slope form of the line is
`y+1=2(x-6)`

Answer 2

`\\ \text{We know that the point-slope for the line passing throught }(x_1, y_1)\\ \text{and having slope m is given by}\\ \\ y-y_1=m(x-x_1)\\ \\ \text{so using this point-slope form of line, the equation of the line passing}\\ \text{through the point }(6,-1)\text{ and having a slope of }m=2\text{ is}\\ \\ y-(-1)=2(x-6)\\ \\ \Rightarrow y+1=2(x-6)\\ \\ \text{this is the required point-slope form of the line.}`

y+1 =2 (x-6)