The slope of a line passing through H (-2, 5) is -3/4. Which ordered pair represents a point on this line?
a. (6, -1)
b. (2, 8)
c. (-5, 1)
d. (1, 1)
I think it's C. And it is NOT B by the way.
What steps did you perform to pick C
Slope is ∆y/∆x = -3/4. That is, for every 4 x increases, y decreases by 3.
C is wrong. It is 3 left, 4 down from (-2,5). C is on a line with slope 4/3. It is on the line perpendicular to the indicated line.
You want 4 left, 3 up or 4 right, 3 down: (-6,8) or (2,2)
Better check for typos.
if you compute the slope for each point , it won't take long
not b ... or c
To determine which ordered pair represents a point on the line with a slope of -3/4 passing through the point H (-2, 5), we can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of the given point H (-2, 5) and m is the slope. By substituting the values, we can find the equation of the line. Then, by checking which of the given options satisfy this equation, we can determine the correct answer.
Using the point-slope formula, the equation of the line passing through H (-2, 5) with a slope of -3/4 is:
y - 5 = (-3/4)(x - (-2))
Simplifying this equation, we have:
y - 5 = (-3/4)(x + 2)
y - 5 = (-3/4)x - 3/2
To obtain the final equation, we can move the constant term (-3/2) to the other side:
y = (-3/4)x - 3/2 + 5
y = (-3/4)x + 7/2
Now, let's check which of the given points satisfy this equation:
a. (6, -1)
Substituting x = 6 and y = -1 into the equation:
-1 = (-3/4)(6) + 7/2
-1 = -9/2 + 7/2
-1 = -2/2
This does not satisfy the equation, so point (6, -1) does not lie on the line.
b. (2, 8)
Substituting x = 2 and y = 8 into the equation:
8 = (-3/4)(2) + 7/2
8 = -3/2 + 7/2
8 = 4/2
This contradicts the equation, so point (2, 8) does not lie on the line.
c. (-5, 1)
Substituting x = -5 and y = 1 into the equation:
1 = (-3/4)(-5) + 7/2
1 = 15/4 + 7/2
1 = 15/4 + 14/4
1 = 29/4
This does not satisfy the equation, so point (-5, 1) does not lie on the line.
d. (1, 1)
Substituting x = 1 and y = 1 into the equation:
1 = (-3/4)(1) + 7/2
1 = -3/4 + 7/2
1 = -3/4 + 14/4
1 = 11/4
This does not satisfy the equation, so point (1, 1) does not lie on the line.
Based on this analysis, none of the given options (a, b, c, or d) represents a point on the line with a slope of -3/4 passing through H (-2, 5). So, it appears that all the given options are incorrect.