Which is the distance between the point with the coordinates (-2, 3) and the line with the equation 6x-y=-3?

Question

whpalmer4 · Answer

Find the slope of line $6x-y=-3$.  Find the slope of a line perpendicular to that line (the product of the two slopes will be -1\).  Now write the equation of a line with that newfound slope that goes through the point $(-2,3)$ using the point-slope formula: $$y-y_1 = m(x-x_1)$$

Find the point where that line intersects with $6x-y=-3$.  You can use the distance formula to find the distance between the two points $(-2,3)$ and the point you just found:
$$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$

anonymous · Answer

okay hold on thanks

anonymous · Answer

so it would be (-2-6)^2+(3-3)^2?

whpalmer4 · Answer

No, it wouldn't be that.  For starters, you didn't take the square root.  Also, you aren't using the right point for the point on the line closest to $(-2,3)$.

Let's check your intermediate steps.  

1) what is the slope of the line $6x-y=-3$?
2) what is the slope of a line perpendicular to that line?
3) what is the equation of a line with the slope in 2) that goes through point $(-2,3)$?
4) where does that line intersect with the line $6x-y=-3$?