Question

What is the slope of a line that contains the point (1,-5) and has the same y-intercept as 2x-y=9?

Answer 1

The slope of the required line is 4.

Explanation:

Let the equation of the line be represented as
`\[y=mx+c\]`

Given line with the same y-intercept is represented as:

`\[2x-y=9\]`

`\[=>y=2x-9\]`

So the intercept of the 2 lines is -9.

Hence, the equation of the required line becomes
`\[y=mx-9\]`

But this line passes through the point (1,-5)

`\[=>-5=m*1-9\]`

`\[=>m=9-5\]`

`\[=>m=4\]`

So the slope of the required line is 4.