Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept form)

Answer:[tex]\displaystyle y=-\frac{1}{2}x+4[/tex]Step-by-step explanation:Equation of a LineWe 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