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:

$m_1=-\frac{1}{m_2}$

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]:

$m_1=-\frac{1}{\frac{7}{4}}\Rightarrow m_1=-\frac{4}{7}$

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=-\frac{4}{7}(x-(-1))\Rightarrow y-4=-\frac{4}{7}x-\frac{4}{7}$$\Rightarrow y=-\frac{4}{7}x+\frac{24}{7}$

And that last function of y is the line m.