9x - 24 + 4x = -24 + 14x - x
13x - 24 = 13x - 24
0 = 0
Answer is All real numbers
Let's start with a picture.
We see RST is smaller, and BC is parallel to but in the opposite direction to its corresponding segment ST. Both have slope -1.
If we look at the difference of points (technically called vectors but we don't have to go there) we get
C-B=(-2,2)
T-S=(1,-1)
Without further calculation we can see T-S is half the length of C-B.
The problem asks for a dilation followed by a reflection. We know the dilation scale is k=1/2 because the new triangle is half the size.
After dilation we get A'B'C':
A'(3,2), B'(-1,0), C'(-2,1)
We see now we need a reflection that flips the coordinates x and y. That's the +45° line through the origin, namely y=x.
Answer: k=1/2, y=x
4x - y + 3 =0 is the equation of the line
Step-by-step explanation:
Given:
The slope of the line = 5
The points through with the line passes = (0,3)
To Find:
The equation of the line =?
Solution:
The equation y = mx + b
where m is the slope and (0,b) is the y-intercept.
The slope is given which is m = 4 and a point (0,3)
Then you can use slope-point equation
where 
is the given point
y - (3) = 4(x - 0)
y - 3 = 4(x)
y = 4x - 22
y - 3 = 4x
4x - y + 3 = 0
The answer to your question is...
<h2>1 5/12 or 17/12</h2>
