Write an equation for the line that is parallel to the given line and passes through the given point.
y = 5x + 10; (2, 14)
A.y=1/5x +4
B.y=-1/5x-4
C.y=5x-68
D.y=5x+4
I think it might be D...not sure
1. D
2. C
3. B
4. C
5. C
1. D
2.C
3.D
4.B
5.D
6.B
7.A
8.C
9.B
10. C
you know it must have slope 5, so that leaves C,D as possibilities.
only D contains the point.
Thank you very much...
Well, let's see if we can figure it out together!
The given line is y = 5x + 10. We're looking for a line that is parallel to this line and passes through the point (2, 14).
Now, lines that are parallel have the same slope. The slope of the given line is 5. So, any line that is parallel to it must also have a slope of 5.
Now let's use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We will substitute x1 with 2, y1 with 14, and m with 5 since the slope is 5.
Plugging in the values, we get:
y - 14 = 5(x - 2)
Now let's simplify it:
y - 14 = 5x - 10
Bringing "y" to the left side, we get:
y = 5x - 10 + 14
Which simplifies to:
y = 5x + 4
So, based on our calculations, the equation of the line that is parallel to y = 5x + 10 and passes through the point (2, 14) is y = 5x + 4.
Therefore, the correct answer is D.
I hope my explanation didn't "slo-p" down your understanding of parallel lines!
To find the equation of a line parallel to a given line, you need to consider two things: the slope of the given line and the point through which the line should pass.
The given line has a slope of 5, which means any line parallel to it will also have a slope of 5. The general equation for a line can be written as y = mx + b, where m represents the slope.
Now we have the slope (m = 5) and the point (2, 14) through which the line should pass. To find the equation, we can substitute these values into the equation and solve for b.
Using the point-slope form of the equation (y - y1 = m(x - x1)), we can write:
y - 14 = 5(x - 2)
Simplifying this equation:
y - 14 = 5x - 10
y = 5x - 10 + 14
y = 5x + 4
So the equation for the line parallel to y = 5x + 10 and passing through the point (2, 14) is y = 5x + 4.
Therefore, the correct answer is D: y = 5x + 4.