The general form of the line is:
y = mx + c where:
m is the slope
c is the y-intercept
Now, we are given that the slope = 1/2.
The equation now became:
y = (1/2) x + c
Now, we need to get the y-intercept. We are given that (-4 ,1) belongs to the line. Therefore, this point satisfies the equation of the line. Based on this, we will substitute with this point in the equation above and solve for c as follows:
y = (1/2) x + c
1 = (1/2)(-4) + c
1 = -2 + c
c = 1+2
c = 3
Based on the above, the equation of the line is:
y = (1/2) x + 3
The points (1, 2) and (4, 2) both have the same y-value, so that is the horizontal line y = 2.
The given point has y-value of 3, so the line passing through it will be
... y = 3
_____
There is no x-term because the slope is 0. We could write it as
... y = 0x +3
but this simplifies to
... y = 3
Answer:
D
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 3, - 6), thus
y = a(x + 3)² - 6
To find a substitute (0, 0) into the equation
0 = 9a - 6 ⇒ a = 
= 
y = (x + 3)² - 6 ← in vertex form
Expand (x + 3)² and distribute by
y = (x² + 6x + 9) - 6
= x² + 4x + 6 - 6
= x² + 4x ← in standard form
