Find the equation of the line through (6,8) which is parallel to the line y=4x−6.

Mathematics

1 answer:

Ratling [72]3 years ago

3 0

Answer:

$y=4x-16$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when x is 0)
Parallel lines always have the same slope

1) Determine the slope (m)

$y=4x-6$

4 is in the place of m, making it the slope. Because parallel lines have the same slope, the slope of the line is therefore 4. Plug this into $y=mx+b$ :

$y=4x+b$

2) Determine the y-intercept (b)

$y=4x+b$

Plug in the given point (6,8) and solve for b

$8=4(6)+b\\8=24+b$

Subtract 24 from both sides to isolate b

$8-24=24+b-24\\-16=b$

Therefore, the y-intercept of the line is -16. Plug this back into $y=4x+b$ :

$y=4x-16$

I hope this helps!

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Type the correct answer in the box. Write the standard form of the quadratic equation modeled by the points shown in the table b

White raven [17]

Y =ax² + bx +c

1) Point (0,7)

7 = a*0² +b*0 +c
c = 7
y=ax² + bx + 7

2) Point (1,4)
4=a*1² + b*1 + 7, ----> 4 = a +b + 7, ------> a+b= - 3
3) Point (2, 5)
5=a*2² + b*2 + 7, ----> 5=4a+2b +7,---> -2=4a+2b, ----> -1=2a + b

4) a+b= - 3, ----> b= -3 - a (substitute in the second equation)
2a+b= -1
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5) a+b= - 3
2 + b = -3
b = -5

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