Answer:
The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]
Step-by-step explanation:
We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line [tex]y=-\frac{1}{3}x+4[/tex]
The general form of point-slope is; [tex]y-y_1=m(x-x_1)[/tex]
where m is slope and [tex](x_1,y_1)[/tex] is the point
We need to calculate slope.
We are given equation of line [tex]y=-\frac{1}{3}x+4[/tex] that is perpendicular to the required line.
The equation is given in slope-intercept form [tex]y=mx+b[/tex] where m is slope.
Comparing both equations we get m= -1/3
But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e [tex]m=-\frac{1}{m}[/tex]
So, slope of required line is m = 3 (opposite reciprocal of -1/3)
Now, the equation in point-slope form having slope m=3 and point (6,-5) is
[tex]y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)[/tex]
So, The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]
