Question

The equation line l is given by the equation y= 7/4x+3. line m goes through the point ( –1,4) and is perpendicular to line l which of the following is the equation of line m ?

Answer 1

We determine line m as follows:

*First, by theorem we have the following:

`m_1=-(1)/(m_2)`

Here m1 & m2 are the slopes of two perpendicular lines. For all lines that are perpendicular that is true, so we calculate the slope of line m using the slope of the function given [Which has a slope of 7/4]:

`m_1=-(1)/((7)/(4))\Rightarrow m_1=-(4)/(7)`

So, the slope of line m is -4/7. Now, using this slope and the point (-1, 4) we replace in the following expression:

`y-y_1=m_1(x-x_1)`

Here x1, y1 & m1 are the x-component of the point, the y-component of the point, and the slope of the line respectively, so we replace and solve for y:

`y-4=-(4)/(7)(x-(-1))\Rightarrow y-4=-(4)/(7)x-(4)/(7)`
`\Rightarrow y=-(4)/(7)x+(24)/(7)`

And that last function of y is the line m.