+980 1. A line with slope 2/3 contains the point P(-18, -12). What is the x-intercept of the line?
2. The graphs of y=|x| and y=-x^2-3x-2 are drawn. For every x, a vertical segment connecting these two graphs can be drawn as well. Find the smallest possible length of one of these vertical segments.
+129852 1. The equation of the line can be found as follows :
y = (2/3) ( x + 18) - 12
To find the x intercept, let y = 0 ......so we have....
0 = (2/3)(x + 18) - 12 add 12 to both sides
12 = (2/3) ( x + 18) multiply both sides by (3/2)
18 = x + 18 subtract 18 from both sides
0 = x ⇒ the x intercept
+129852 2. The graphs of y=|x| and y=-x^2-3x-2 are drawn. For every x, a vertical segment connecting these two graphs can be drawn as well. Find the smallest possible length of one of these vertical segments.
Look at the graph here : https://www.desmos.com/calculator/p7iq0yf8z5
Note that the vertex of the parabola occurs at (-1.5, .25)
When a vetical ine is drawn at x = -1.5, the line will intersect the absolute value graph at (-1.5, 1.5)
So......the distance between these two points is
1.5 - .25 =
1.25 units
