Which of the following equations represents the equation for the line that is parallel to the given line and passes through the given point?
y= 1/5 x - 10; (15, -16)
A. y = -5x +19
B. y = 1/5x + 91/5
C. y = 1/5 x - 19
D. y = 5x - 19
I do know that to be parallel the slopes need to be the same. Please explain how you solve this.
try it in B
y = 1/5 x + 91/5
plug in (15,-16)
-16 = (1/5)(15) + 91/5
-16 = 3 + 91/5 , which is not true,
so it better be C
y = 1/5 x - 19
-16 = (1/5)(15) - 19
-16 = 3-19
-16 = -16 , ahhh that's true, so it must be C
Thank you so much for explaining it in detail. I really appreciate it.
Well, looks like we've got a math problem on our hands! Don't worry, I'll do my best to solve it using my hilarious math skills.
To find the equation of a line that is parallel to the given line, we know that it must have the same slope as the given line. So, let's start by determining the slope of the given line.
The given line has a slope of 1/5, which means any line parallel to it must also have a slope of 1/5.
Now, we have to find the equation of the line that passes through the given point (15, -16). To do this, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
(y - (-16)) = (1/5)(x - 15)
Simplifying this equation, we get:
y + 16 = (1/5)x - 3
Subtracting 16 from both sides, we have:
y = (1/5)x - 19
So, the equation of the line that is parallel to the given line and passes through the given point is y = (1/5)x - 19. That means the answer is option C, which stands for "Clown-tastic choice!"
Hope that brings a smile to your face!
To find the equation of a line that is parallel to a given line and passes through a specific point, you need to use the same slope as the given line but substitute the coordinates of the given point into the equation.
In this case, the given line is y = (1/5)x - 10, which means the slope is 1/5. We want to find the equation of a line that is parallel to this line, so the slope of the parallel line will also be 1/5.
Now, substitute the coordinates of the given point, (15, -16), into the equation y = (1/5)x + b, where b is the y-intercept we need to find.
Plugging in the x-coordinate (15) and y-coordinate (-16) into the equation and solving for b, we get:
-16 = (1/5)(15) + b
-16 = 3 + b
b = -19
Therefore, the equation of the line that is parallel to the given line and passes through the given point is y = (1/5)x - 19.
Among the given options:
A. y = -5x + 19 (slope is -5, not the same as 1/5)
B. y = (1/5)x + 91/5 (slope is 1/5, same as the original line, but y-intercept is different)
C. y = (1/5)x - 19 (correct equation)
D. y = 5x - 19 (slope is 5, not the same as 1/5)
So the correct answer is C. y = (1/5)x - 19.
Since the slope must be the same, it limits it to
choices B or C, since both have 1/5 as the slope
so plug in the given point to see which one satisfies the equation