Yep, another math question!
The slope of a line passing through H ( -2, 5) is -3/4, which ordered pair represents a point on the line?
A: (6, -1)
B:(2, 8)
C: (-5, 1)
D:(1, 1)
No graph was with the question btw. I tried making a coordinate plane myself and making lines to see if any of these points were there. Haven't found any tbh. But I'm sure I'm doing it wrong. I think maybe A or B is right
slope AH = (5+1)/(-2-6) = 6/-8 = -3/4 <----- winner
slope BH = (5-8)/(-2-2) = -3/-4 = 3/4 <---- wrong sign
another way, but longer way, is to find the equation of the line using the given data,
then subbing in each of the points to see if it satisfies.
You should try it just for fun.
Thanks, I'll be sure to try using that from now on.
To find the point on the line passing through the point H(-2, 5) with a slope of -3/4, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Let's substitute the values into the equation:
y - 5 = (-3/4)(x - (-2))
Simplifying the equation:
y - 5 = (-3/4)(x + 2)
Multiplying both sides of the equation by 4 to eliminate the fraction:
4(y - 5) = -3(x + 2)
Expanding the equation:
4y - 20 = -3x - 6
Rearranging the equation to the standard form:
3x + 4y = -14
Now, we can substitute the x and y values of each given point to check which one satisfies the equation:
A: (6, -1)
3(6) + 4(-1) = -14
18 - 4 = -14
14 = -14
The equation is not satisfied, so point A is not on the line.
B: (2, 8)
3(2) + 4(8) = -14
6 + 32 = -14
38 = -14
The equation is not satisfied, so point B is not on the line.
C: (-5, 1)
3(-5) + 4(1) = -14
-15 + 4 = -14
-11 = -14
The equation is not satisfied, so point C is not on the line.
D: (1, 1)
3(1) + 4(1) = -14
3 + 4 = -14
7 = -14
The equation is not satisfied, so point D is not on the line.
Therefore, none of the given points A, B, C, or D are on the line passing through H(-2, 5) with a slope of -3/4.
To determine which ordered pair represents a point on the line with a given slope passing through H(-2, 5), we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, m is the slope, and (x, y) is any point on the line.
In this case, we have H(-2, 5) and a slope of -3/4. Substituting these values into the point-slope form, we get:
y - 5 = (-3/4)(x - (-2))
Simplifying further:
y - 5 = (-3/4)(x + 2)
Now let's solve this equation for each ordered pair and see which one satisfies it.
For option A: (6, -1)
-1 - 5 = (-3/4)(6 + 2)
-6 = (-3/4)(8)
-6 = -6
The equation is satisfied for option A.
For option B: (2, 8)
8 - 5 = (-3/4)(2 + 2)
3 = (-3/4)(4)
3 = -3
The equation is not satisfied for option B.
For option C: (-5, 1)
1 - 5 = (-3/4)(-5 + 2)
-4 = (-3/4)(-3)
-4 = -9/4
The equation is not satisfied for option C.
For option D: (1, 1)
1 - 5 = (-3/4)(1 + 2)
-4 = (-3/4)(3)
-4 = -9/4
The equation is not satisfied for option D.
Therefore, the point that corresponds to a point on the line with a slope of -3/4 passing through H(-2, 5) is option A: (6, -1).