Answer: c.(3, 25) and (7, 9)
y = –x^2 + 6x + 16 and y = –4x + 37
Plug in -4x+37 for y in first equation . It becomes
Combine like terms. add 4x and subtract 37 on both sides
Divide the whole equation by -1 to remove negative sign from -x^2
Now factor the left hand side
(x-7)(x-3) = 0
x-7 =0 and x-3=0
x= 7 and x=3
Now we find out y using y = –4x + 37
when x= 7 , then y=-4(7) +37 = 9
when x= 3, then y=-4(3) + 37 = 25
We write solution set as (x,y)
(7,9) and (3,25) is our solution set
Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
<u>Point-slope form:</u>
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line=
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
Thus the equation of the line is .
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
=
When x=3, y=3,
Thus the equation of the line is .