Question

Help I'm confused!!!!

A line passes through the points (5, –7.5) and has a y-intercept 10.
Which is a linear function in the form of y = mx + b for this line?

Answer 1

`y = mx + b` form of line passing through (5, –7.5) and line having x y-intercept of 10 is
`y= -3.5x+10`

Solution:

Need to find the equation of a line in form of
`y = mx + b`

Given that

Line is passing through point (5, –7.5) and y intercept of line = 10

y intercept is a point where line crosses the y axis.

In our case line have y intercept of 10, which means line crosses y axis at 10. Also at y axis, value of x is always 0.

So we can say that line passes through point (0, 10).

Now we can say that we need equation of line passing through (5, –7.5) and (0, 10).

Equation of line passing through point
`\left(x_(1), y_(1)\right)` and
`\left(x_(2), y_(2)\right)` is given by

`y-y_(1)=(\left(y_(2)-y_(1)\right))/(\left(x_(2)-x_(1)\right))\left(x-x_(1)\right)`

In our case
`x_(1)=5; y_(1)=-7.5; x_(2)=0; y_(2)=10`

Substituting given value in (1) we get

`\begin{array}{l}{y-(-7.5)=((10-(-7.5)))/((0-5))(x-5)} \\\\ {\Rightarrow y+7.5=-(17.5)/(5)(x-5)} \\\\ {\Rightarrow y+7.5=-(17.5)/(5)(x-5)} \\\\ {\Rightarrow y+7.5=-3.5(x-5)} \\\\ {\Rightarrow y=-3.5 x+17.5-7.5} \\\\ {\Rightarrow y=-3.5 x+10}\end{array}`

Hence
`y = mx + b` form of line passing through (5, –7.5) and line having x y-intercept of 10 is
`y= -3.5x+10`.