"Undefined" slope means the line on the graph is vertical, and that
tells the whole story right there. The 'x' coordinate is the same for
every point on the line. If (6, -1) is a point on the line, then you know
that the x-value of EVERY point on it is 6 .
It's a vertical line that intersects the x-axis at x=6, and the equation
of the line is x=6 .
9x+1+32x+1=36
Combine like terms
41x+2=36
Subtract 2 from both sides
41x=34
X= 41/34 or 1.2
You need to find where the discriminant is less than zero
Remember the discriminant is b^2 - 4ac
a = m
b = -5
c = -2
Set up the inequality like this
(-5)^2 - 4m(-2) < 0
25 + 8m < 0
8m < -25
m < -25/8 < -3.125
So any number less than -3.125 will make this graph have no x-intercepts (or real roots)
38/5 is the answer to the question
The given plane has normal vector

Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation

This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when

which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of
).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
