This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
The last part is not there
Step-by-step explanation:
Yes that is true, all opposite sides would be parallel, and all the corners are 90 degrees, then yes it is true
Answer:
x - 5y = 22
Step-by-step explanation:
Step 1: rewrite the equation of the given line in to slope-intercept form by solving for y
x = 5y - 9
-5y = -x - 9 (subtract 5y and x from both sides)
y = x/5 + 9/5 (divide both side by -5)
Step 2: Our line is parallel to this line, so it has the same slope, but a different y-intercept, so set up the equation...
y = x/5 + b
We are given a point (x, y) of (2, -4), so plug that in and solve for b.
-4 = 2/5 + b
-4 - 2/5 = b (subtract 2/5 from both sides to isolate b)
-20/5 - 2/5 = b
-22/5 = b (simplify)
So the equation of our line is y = x/5 - 22/5
Step 3: Standard form is ax + by = c, where a is a positive integer
subtract x/5 from both sides...
-x/5 + y = - 22/5
multiply by -5 so x becomes a positive integer
x - 5y = 22
