Question

1. A straight line has a gradient of 4/5. If the line passes through the points p (7, m+1) and Q (m, -1) find the value of m​

Answer 1

To find the value of
`\displaystyle\sf m`, we can use the slope formula, which states that the gradient (or slope) of a line passing through two points
`\displaystyle\sf (x_(1),y_(1))` and
`\displaystyle\sf (x_(2),y_(2))` is given by:

`\displaystyle\sf \text{{Gradient}}=(y_(2)-y_(1))/(x_(2)-x_(1))`

In this case, we have the following points:

Point P:
`\displaystyle\sf (7,m+1)`

Point Q:
`\displaystyle\sf (m,-1)`

We are given that the gradient of the line is
`\displaystyle\sf (4)/(5)`. So, we can set up the equation:

`\displaystyle\sf (4)/(5)=((-1)-(m+1))/(m-7)`

To simplify the equation, we can multiply both sides by
`\displaystyle\sf m-7` to eliminate the denominator:

`\displaystyle\sf 4(m-7)=5(-1-(m+1))`

Now, let's solve for
`\displaystyle\sf m`:

`\displaystyle\sf 4m-28=-5(-1-m-1)`

`\displaystyle\sf 4m-28=-5(-2-m)`

`\displaystyle\sf 4m-28=10+5m`

`\displaystyle\sf 4m-5m=10+28`

`\displaystyle\sf -m=38`

`\displaystyle\sf m=-38`

Therefore, the value of
`\displaystyle\sf m` is
`\displaystyle\sf -38`.

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