Answer:
y = 3x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← x and y- intercepts
m = 
= 
= 3
The line crosses the y- axis at (0, 3) ⇒ c = 3
y = 3x + 3 ← equation of line
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
The unit rate of gas usage is 35 miles per gallon.
Step-by-step explanation:
"Unit rate" refers to the number of miles for 1 gallon.
<u>From the graph given</u>,
it can be determined that, the car goes 2 miles for 70 gallons and 3 miles for 105 gallons.
To find miles per gallon, <u>use rate formula</u>
Rate= <em>Given miles/ Given gallons</em>= 2/70
Unit Rate= <em>miles/ 1 gallon</em>= X/1
where "X" term refers to number of miles per gallon.
By Comparing the rates we get,
2/70 =X/1
<u>X=35 miles per gallon</u>
Similarly,
3/105 =X/1
<u>X=35 miles per gallon</u>
Answer:
not understanding meaning of your question
Step-by-step explanation:
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