Can someone please help me?
choose the point-slope form of the equation below that represents the line passes through the point (-1,6) and has a slope of -3
a) y-6=-3x-3
b) y-6=-3(x+1)
c) y=-3x+3
d) 3x+y=3
I think it is c but I don't know.
c is slope-intercept.
The point slope form of the line through (h,k) with slope m is
y-k = m(x-h)
any other choices look like that?
Yeah, it's C
Bzzzt. but thanks for playing.
To find the point-slope form of an equation representing a line, you need to use the coordinates of a point on the line and its slope. Let's go through the options one by one:
a) y-6=-3x-3
To determine if this equation represents the line passing through the point (-1, 6) with a slope of -3, we can rearrange it into the point-slope form y - y1 = m(x - x1). Comparing this equation to the given form, we have:
y - 6 = -3x - 3
This equation does not match the point-slope form; the constant term should be -3, but here it is -3-6 = -9. Therefore, option a is incorrect.
b) y-6=-3(x+1)
Comparing this equation to the point-slope form, we find:
y - 6 = -3(x + 1)
Again, this equation does not match the point-slope form since the constant term is not -3. Thus, option b is also incorrect.
c) y=-3x+3
Now let's examine this equation:
y = -3x + 3
This equation is already in slope-intercept form (y = mx + b), not in point-slope form. Therefore, it is not the correct answer.
d) 3x+y=3
Finally, let's check the last option:
3x + y = 3
To transform this equation into point-slope form, we need to solve for y:
y = -3x + 3
Now this equation matches the point-slope form, where the slope is -3 and the point (-1, 6) lies on the line. Therefore, option d is the correct answer.
In conclusion, the correct choice that represents the line passing through the point (-1,6) with a slope of -3 is option d) 3x + y = 3.