1. Find the slope of the line through the pair of points.
(-1/3,0) and (-1/2,-1/2)
Choices:
-3
1/3
-1/3
3
2. Write in standard form an equation of the line passing through the given point with the given slope.
Slope=8/7; (5,-3)
Choices:
-8/7x+y=-61/7
-8/7x-1=-61/7
-8/7x+y=61/7
8/7x+y=-61/7
You're more likely to get help if you post what you think are the answers.
slope = difference in y values/difference in x values
= (-1/2 - 0)/(-1/2 + 1/3)
= (-1/2) / (-1/6)
= (1/2)(-6) = 3
2. y = (8/7) + b
sub in the given point
-3 = (8/7)(5) + b
multiply by 7
-21 = 40 + 7b
b = -61/7
y = (8/7)x - 61/7 or
(8/7)x - y = 61/7
better form would be
8x - 7y = 61
btw, none of your answers match with
(8/7)x - y = 61/7 which is the answer in the form of the other answers.
I would not consider any of the given answers to be in standard form
Most text books consider "standard" form to be in the form
ax + by = c, where a,b, and c are integers.
My first line of #2 should have been
2. y = (8/7)x + b
yeah, i agree with reiny
To find the slope of a line passing through two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's apply this formula to find the slope of the line passing through (-1/3, 0) and (-1/2, -1/2):
x1 = -1/3
y1 = 0
x2 = -1/2
y2 = -1/2
slope = (-1/2 - 0) / (-1/2 - (-1/3))
= (-1/2) / (-1/2 + 1/3)
= (-1/2) / (-3/6 + 2/6)
= (-1/2) / (-1/6)
= (-1/2) * (-6/1)
= 6/2
= 3
Therefore, the slope of the line passing through (-1/3, 0) and (-1/2, -1/2) is 3.
Now let's move on to the second question. To write the equation of a line given a point and a slope, you can use the slope-intercept form equation:
y = mx + b
where m is the slope and b is the y-intercept. We need to find the value of b using the given point (5, -3) and slope 8/7.
Substituting the values into the equation, we get:
-3 = (8/7)(5) + b
Now solve for b:
-3 = 40/7 + b
To isolate b, subtract 40/7 from both sides:
-3 - 40/7 = b
(-21/7 - 40/7) = b
-61/7 = b
Therefore, b = -61/7.
The equation of the line passing through the point (5, -3) with slope 8/7 can be written in standard form as:
8/7x + y = -61/7
So the correct choice is 8/7x + y = -61/7.