Multi step equations 4x+6+3=17
2 answers:
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Answer:
The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal" ⇒ A
Step-by-step explanation:
- Parallel lines have equal slopes and different y-intercepts
- The rule of the slope of a line passes through points (x1, y1) and (x2, y2) is m =
In the given figure
∵ The blue line passes through points A and B
∵ A = (-4, -2) and B = (4, 4)
∴ x1 = -4 and y1 = -2
∴ x2 = 4 and y2 = 4
→ Substitute them in the rule of the slope
∵ m(AB) = =
=
=
∴ The slope of line AB is
∵ The green line passes through points C and D
∵ C = (0, -3) and D = (4, 0)
∴ x1 = 0 and y1 = -3
∴ x2 = 4 and y2 = 0
→ Substitute them in the rule of the slope
∵ m(CD) = =
=
∴ The slope of line CD is
∵ The slope of line AB = the slope of line CD
∵ Parallel lines have the same slope
∴ AB // CD
∴ AB and CD are parallel lines
The best statement which explains the relationship between lines AB and CD is "They are parallel because their slopes are equal"
Answer:
Step-by-step explanation:
Let g be the number of games James plays and t be the number of tokens James has.
We will write our function's formula in slope-intercept form of equation.
, where,
m = Slope of line,
b = y-intercept.
We have been given that initially James has 20 tokens. This means that before playing the games James has 20 tokens or at g equals 0 t equals 20. So our y-intercept will be 20.
We are also told that after playing the game 3 times, he has 8 tokens remaining.
Let us find the slope of line using points (3,8) and (0,20).
, where,
m = Slope of line,
= Difference between two y-coordinates,
= Difference between x-coordinates of same two y-coordinates.
Upon substituting coordinates of our given points we will get,
So the slope of our line will be -4.
We can see that number of remaining tokens are dependent on number games James plays, this mean that t is a function of g.
Upon substituting our values in slope-intercept form of equation we will get,
, where, t(g) represents number of tokens James has left after playing g games.
Therefore, our required function will be .