Find the linear function satisfying the given conditions.
g(2) = 9 and the graph of g is perpendicular to the line 4x − 2y = 3.
g(x) =
To find the linear function g(x) satisfying the given conditions, we need to use the information provided about the point and the perpendicular line.
First, let's find the slope of the line 4x - 2y = 3 by rearranging it into the slope-intercept form (y = mx + b). Rearranging the equation:
4x - 2y = 3
-2y = -4x + 3
y = 2x - 3/2
We can see that the slope of this line is 2.
Since the graph of g is perpendicular to this line, the slope of g will be the negative reciprocal of 2. In other words, the slope of g will be -1/2.
Now we have the slope of g, and we also know that g(2) = 9. We can use this information to find the y-intercept (b) of g by substituting it into the slope-intercept form (y = mx + b) and solving for b.
Using the point-slope form of a linear equation: y - y1 = m(x - x1)
Substituting the coordinates (x1, y1) = (2, 9) and the slope m = -1/2:
y - 9 = (-1/2)(x - 2)
y - 9 = (-1/2)x + 1
y = (-1/2)x + 10
So the linear function g(x) that satisfies the given conditions is g(x) = (-1/2)x + 10.
the line 4x − 2y = 3
has slope = 2
so, you want a line with slope = -1/2. Now you have a point (2,9) and a slope (-1/2), so your line is
g-9 = -1/2 (x-2)