Answer:
y = -2x + 10
Step-by-step explanation:
In order to know this, first you need to know when two lines are perpendiculars. In this case, two lines are perpendiculars when the products of their pendings are equals to -1.
According to the above, if we have the 2nd equation which is y = x/2 + 3, we can know that the pending is 1/2 (The number next to the x will always be the pending of the line).
So, two lines would be perpendiculars when their products is -1 so:
1/2 * m = -1
solving for m:
1 * m = 2*(-1)
m = -2
With this, we know that the pending of the first line is -2 and we can assume that the first element of the equation of this line begins like this: y = -2x + b
However we need to know the y intercept or cut point of this line (i call it b here). We can also know this, because we have one point of this line, which is (1,8). These are the values of x and y respectively so, let's replace them in the equation above and solve for the cut point:
y = -2x + b
b = y + 2x
replacing 1 and 8 we have:
b = 8 + 2(1)
b = 10
Therefore, we can conclude that the equation of the line that passes through that point and is perpendicular to x/2 + 3 is:
y = -2x + 10
