When a line and a curve are tangent to each other, they are joined together by 1 point (x,y). So, you equate both equations either in terms of x or y. For this problem, let's equate in terms of y.
y = k - x
y = x² + 3x + 1
k - x = x² + 3x + 1
k = x² + 3x + x + 1
k = x² + 4x + 1
This would be the value of k. Since we are not given the common point, it can only be expressed in terms of x or y.
<u>Answer</u>
y = -2x + 10
<u>Explanation</u>
The general equation for a straight line is y = mx + c where m and c are gradient and y-intercept respectively.
y=x/2+3 = y (1/2)x + 3
gradient = 1/2
Gradient of the line perpendicular to y=x/2+3 is;
m × 1/2 = -1
m = -2
Now we find the equation of a line passing through (1,8) and have a gradient of -2.
-2 = (y - 8)/(x - 1)
-2(x - 1) = (y - 8)
2 -2x = y - 8
y = -2x + 10
Answer:
it is not factorable
Step-by-step explanation:
it is not factorable
