Respuesta :
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
If two lines are perpendicular, their slopes are the inverse multiplied by (-1)
If a line has a slope of m, then the slope of a line perpendicular to it is:
[tex]Slope\text{ }perpendicular=-\frac{1}{m}[/tex]We know that the slope of the perpendicular line is 1/2, then the slope of the line we are calculating is:
[tex]m=-\frac{1}{\frac{1}{2}}=-2[/tex]Now, we can use the point-slope form of a line. Given a point P and a slope m, the equation of the line with slope m that passes through the point P is:
[tex]\begin{gathered} P=(x_P,y_P) \\ . \\ y=m(x-x_P)+y_P \end{gathered}[/tex]In this case, the slope is m = -2 and passes through the point P = (2, 7)
We write:
[tex]y=-2(x-2)+7[/tex]If we simplify this expression we get the equation of the line in slope-intercept form:
[tex]y=-2x-2(-2)+7=-2x+4+7=-2x+11[/tex]Thus, the answer is:
[tex]y=-2x+11[/tex]