Answer:
y = [tex]\frac{1}{2} x[/tex] + 3
Step-by-step explanation:
To find the equation that passes through the points (6,1) and is perpendicular to the line whose equation is y = -2x - 6, we are going to follow the steps below;
First, we determine the slope of the equation:y = -2x - 6, only then can we find the slope of our perpendicular equation.
y = -2x - 6
m = -2
The slope of the above line is -2
So, the slope of the perpendicular line to y = -2x - 6 will have a slope equals to the negative reciprocal , that is; [tex]m_{1} m_{2}[/tex] = -1
The slope(m) of our perpendicular equation is [tex]\frac{1}{2}[/tex] using the above formula.
Haven gotten our slope, next is for us to find our intercept
To get the intercept, we will use this standard equation;
y = mx + c
where m =slope(our new slope=1/2) c=intercept x and y are the two points through which the line passes through. That is; x=6 and y=1. So we are going to plug in all this variable into the standard equation;
y = mx + c
1 = [tex]\frac{1}{2}[/tex](6) + c
1 = 3 + c (six will divide two to give us three)
To get the value of c, subtract 3 from both-side of the equation
1 - 3 = 3+ c -3
-2 = c
c = -2
Therefore, our new intercept is 3
So we can now plug in our new slope and intercept into y=mx+c
y = [tex]\frac{1}{2} x[/tex] + 3
We can re-arrange it;
- [tex]\frac{1}{2} x[/tex] + y = 3
