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
Thanks full answers would be great!
1. To find the slope of the line passing through the given points (-1/3, 0) and (-1/2, -1/2), you can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let's plug in the values from the given points:
x1 = -1/3, y1 = 0
x2 = -1/2, y2 = -1/2
Plugging the values into the slope formula:
slope (m) = (-1/2 - 0) / (-1/2 - (-1/3))
= (-1/2) / (-1/2 + 1/3)
To simplify the expression in the denominator, you need to find the least common denominator (LCD) of -1/2 and 1/3, which is 6:
(-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 the given points is 3.
2. To write the equation of the line passing through the point (5, -3) with a slope of 8/7, you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of the given point, and m is the slope.
Let's plug in the values from the given point (5, -3) and slope 8/7:
x1 = 5, y1 = -3
m = 8/7
Plugging the values into the point-slope form:
y - (-3) = (8/7)(x - 5)
y + 3 = (8/7)(x - 5)
To convert this equation to standard form (Ax + By = C), you can multiply both sides of the equation by 7 to clear the fraction:
7(y + 3) = 7(8/7)(x - 5)
7y + 21 = 8(x - 5)
7y + 21 = 8x - 40
Now, rearrange the equation to match the standard form:
8x - 7y = 61
So the equation of the line passing through the point (5, -3) with a slope of 8/7 in standard form is 8x - 7y = 61.