1. ## Linear Equations

Hey guys, I have 2 quick questions here on linear algebra.

1) Find the slope-intercept equation of the line that passes through the intercepts of $y=x^2 - 2x +6$ and $y=2(x-1)^2 + 1$

I'm lost on the wording I guess, these two parabolas do not intercept the x-axis at all, and the line that passes through both the y intercepts would just be the y-axis?

Also, I thought maybe it meant throught the 2 points that the parabolas intersect each other, but that's just the line $y=0x+9=9$

I must just be making this too hard on myself. :/

Secondly, I have;

2) Given point $A(-2,-2)$ and line $3x+2y+1=0$, find the shortest distance from point A to the line.

Don't I need the closest point on the line to the point to find the shortest distance? Or should I just leave my distance in terms of the x and y in the linear equation?

2. Originally Posted by superduper
Hey guys, I have 2 quick questions here on linear algebra.

1) Find the slope-intercept equation of the line that passes through the intercepts of $y=x^2 - 2x +6$ and $y=2(x-1)^2 + 1$

I'm lost on the wording I guess, these two parabolas do not intercept the x-axis at all, and the line that passes through both the y intercepts would just be the y-axis?

Also, I thought maybe it meant throught the 2 points that the parabolas intersect each other, but that's just the line $y=0x+9=9$

I must just be making this too hard on myself. :/

Secondly, I have;

2) Given point $A(-2,-2)$ and line $3x+2y+1=0$, find the shortest distance from point A to the line.

Don't I need the closest point on the line to the point to find the shortest distance? Or should I just leave my distance in terms of the x and y in the linear equation?
1) You're menat to find the coordinates of the intersection points of the two given parabolas. To do this, start by solving $x^2 - 2x +6 = 2(x-1)^2 + 1$.

2) The shortest distance will be the distance between the given point and the point on the given line such that line joining those two points is perpendicular to the given line. So first you need to find that point on the line ....