Choose the correct rule for the graph shown. A) y = 2x B) y = 3x + 1 C) y = 2x + 1 D) y = 2x - 1
1 answer:
<h2>Explanation:</h2><h2></h2>
No graph has been provided, but I've provided the graph shown below. Recall that the slope intercept form of the equation of a line is given by:
First of all, the y-intercept of this graph lies on the point:
So our correct option could be either B) or C) because the y-intercept in those cases lies also on the point . If you lies on this point and walk 1 units horizontally, then the y-coordinate runs 3 units up until it gets point
. Therefore, the slope of this line is
In conclusion, this graph is represented by the equation:
B) y = 3x + 1
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Answer:
3rd option
Step-by-step explanation:
( factorise numerator and denominator )
3x² - 3 ← factor out 3 from each term
= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 1
= x² - 1²
= (x - 1)(x + 1) , then
3x² - 3 = 3²(x - 1)(x + 1) ← in factored form
--------------------------------
x² - 5x + 4
consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)
the factors are - 1 and - 4 , since
- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then
x² - 5x + 4 = (x - 1)(x - 4)
then
=
← in factored form