The given equation is:
ax + by = 12
We are given that the two points (6,0) and (3,2) belong to this line. This means that these two points satisfy the equation of the line.
Therefore, to get the value of a and b, we will substitute with the given points in the equation and solve the resulting equations for a and b as follows:
For the point (6,0):
ax + by = 12
a(6) + b(0) = 12
6a = 12
a = 12/6 = 2
For point (3,2):
ax + by = 12
(2)(3) + b(2) = 12
6 + 2b = 12
2b = 12-6 = 6
b = 3
Based on the above calculations:
a = 2 and b = 3, therefore, the equation is:
2x + 3y = 12
Answer:
-5/8
Step-by-step explanation:
Step 1: Find the slope of line d. As we move from point (5, 2) to point (10, 10), x increases by 5 and y increases by 8. Thus, the slope of line d is
m = rise / run = 8/5.
Step 2: Find the negative reciprocal of this m = 8/5. Doing so will give us the slope of line e or of any other line perpendicular to line d:
Slope of line e: -(5/8) = -5/8
Solve for
x
x
by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
x
<
7
x
<
7
Interval Notation:
(
−
∞
,
7
)
