Use the equation and given point to answer the questions below.
The equation of line a is y=12x−1, and it passes through point (6,2).
Line b is perpendicular to line a, and it passes through point (−6,2).
A: What is the slope of line b?
B: What is the y-intercept of line b?
Select two answers: one for A and one for B.
B: 14
B: 1
A: 1/2
A: −2
A: −1/2
B: 5
A: 2
B: -1
a: -2
b: -10
Recall that lines with slopes m1 and m2
are parallel if m1 = m2
are perpendicular if m1 * m2 = -1
so, since line A has slope 1/2, B has slope -2
Now for line B, you have a point (-6,2) and a slope (-2). Using the point-slope form, that makes B's equation
y-2 = -2(x+6)
Rearrange that into the slope-intercept form, and you have
y = -2x - 10
the y-intercept is seen to be -10
A straight line in the form y = mx + b, has a slope of m and a y-intercept of b
so y = (1/2)x - 1 has a slope of 1/2 and a y-intercept of -1
Parallel lines have the same slope, so the slope of your new line is also 1/2
and it must be y = (1/2)x + b, but it passes through the new point (-6,2)
then 2 = (1/2)(-6) + b
2 = -3 + b
b = 5
so your 2nd line equation is y (1/2)x + 5
fit it all together to answer your question
argghhh, I read it as parallel
so go with oobleck's way
perpendicular lines have negative reciprocal slope. for line b slope then is -2. What is the y-intercept of line b? y=-2x+b and the point (−6,2) is one it, then
2=-2(-6)+b or b= 12+2 = 14
Sorry line A is Y=1/2x-1
What is the answer?
To find the slope of line b, we first need to find the slope of line a because line b is perpendicular to line a. The equation of line a is given as y = 12x - 1. We can see that the coefficient of x is the slope of line a. Therefore, the slope of line a is 12.
Since line b is perpendicular to line a, we know that the slopes of line a and line b are negative reciprocals of each other. To find the slope of line b, we can take the negative reciprocal of the slope of line a. The negative reciprocal of 12 is -1/12, therefore the slope of line b is -1/12.
Next, to find the y-intercept of line b, we can use the point (−6,2) that line b passes through. We substitute the x and y coordinates of the point into the equation y = -1/12x + b and solve for b.
Using the coordinates (−6,2), we get:
2 = -1/12*(-6) + b
2 = 1/2 + b
b = 2 - 1/2
b = 4/2 - 1/2
b = 3/2
Therefore, the y-intercept of line b is 3/2.
So the correct answers are:
A: The slope of line b is -1/12
B: The y-intercept of line b is 3/2