Answer:
[tex]\displaystyle y=-\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Equation of a Line
We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.
We are given a line
[tex]y - 12 = 2x -8[/tex]
And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y
[tex]y = 2x +4[/tex]
The coefficient of the x is the slope
[tex]m=2[/tex]
The slope of the perpendicular line is the negative reciprocal of m, thus
[tex]\displaystyle m'=-\frac{1}{2}[/tex]
We know the second line passes through (2,3). That is enough information to find the second equation:
[tex]y-y_o=m'(x-x_o)[/tex]
[tex]\displaystyle y-3=-\frac{1}{2}(x-2)[/tex]
Operating
[tex]\displaystyle y=-\frac{1}{2}(x-2)+3[/tex]
Simplifying
[tex]\displaystyle y=-\frac{1}{2}x+4[/tex]
That is the equation in slope-intercept form. Intercept: y=4
