Answer:
[tex]y=-4x+15[/tex]
Step-by-step explanation:
The correct question is
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=(x/4)+5 ?
step 1
Find out the slope of the given line
we have
[tex]y=\frac{1}{4}x+5[/tex]
so
the slope is
[tex]m=\frac{1}{4}[/tex]
step 2
Find out the slope of the line perpendicular to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=\frac{1}{4}[/tex]
substitute
[tex]\frac{1}{4}*m_2=-1[/tex]
[tex]m_2=-4[/tex]
step 3
Find the equation of the line
The equation of the line in point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
we have
[tex](x_1,y_1)=(2,7)[/tex]
[tex]m=-4[/tex]
substitute
[tex]y-7=-4(x-2)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y-7=-4x+8[/tex]
[tex]y=-4x+8+7[/tex]
[tex]y=-4x+15[/tex]
