Question

HELPPP ITS AN EMERGENCY!!!!!!

Answer 1

Answer:

The equation in point-slope is $\mathbf{y+5=3(x-6)}$

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 $y=-\frac{1}{3}x+4$

The general form of point-slope is; $y-y_1=m(x-x_1)$

where m is slope and $(x_1,y_1)$ is the point

We need to calculate slope.

We are given equation of line $y=-\frac{1}{3}x+4$ that is perpendicular to the required line.

The equation is given in slope-intercept form $y=mx+b$ 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 $m=-\frac{1}{m}$

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

$y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)$

So, The equation in point-slope is $\mathbf{y+5=3(x-6)}$