Answer:
[tex]y=2x-28[/tex]
Step-by-step explanation:
Slope intercept form:
[tex]y=mx+b[/tex]
where:
When two lines are perpendicular, their slopes will be opposite reciprocals.
examples:
[tex]\frac{1}{3}[/tex] → flip the fraction and change the sign → [tex]-3[/tex]
-5 or [tex]-\frac{5}{1}[/tex]→ flip the fraction and change the sign → [tex]\frac{1}{5}[/tex]
[tex]\frac{5}{7}[/tex] →flip the fraction and change the sign →[tex]-\frac{7}{5}[/tex]
So find the opposite reciprocal of the given slope:
[tex]y=(slope)x+(y-intercept)\\\\y=-\frac{1}{2} x-3\\\\slope=-\frac{1}{2}[/tex]
Flip the fraction and change the sign:
[tex]-\frac{1}{2}[/tex] → [tex]\frac{2}{1}[/tex] or [tex]2[/tex]
Now insert the new slope and the given points into point-slope form:
[tex]y-y_{1}=m(x-x_{1})\\\\(14_{x_{1}},0_{y_{1}})\\\\y-0=2(x-14)[/tex]
Solve the equation for y. Use the distributive property:
[tex]y-0=2(x)+2(-14)\\\\y-0=2x-28[/tex]
Simplify:
[tex]y=2x-28[/tex]
:Done
