On coordinate plane, points (2, 1), (1, 5) and (0, 9) are connected through a line.
Drag a number to each box to represent the equation of the line.
y = x +
-9
-5
-4
-2
-1
0
1
2
4
5
9
The equation of the line connecting points (2, 1), (1, 5) and (0, 9) is:
y = -4x + 9
are you sure
Apologies for the confusion. I made an error in my response. Let's re-evaluate the equation of the line.
To find the equation of the line that passes through points (2, 1), (1, 5), and (0, 9), we can use the point-slope form of a linear equation.
First, calculate the slope using the formula:
m = (y2 - y1)/(x2 - x1)
Let's use the first two points, (2, 1) and (1, 5), to find the slope:
m = (5 - 1)/(1 - 2)
= 4/-1
= -4
Now, choose one of the given points (let's use (2, 1)) and substitute its coordinates and the slope into the point-slope form:
y - y1 = m(x - x1)
y - 1 = -4(x - 2)
Simplifying further:
y - 1 = -4x + 8
y = -4x + 9
So, the correct equation for the line passing through the given points is:
y = -4x + 9
The graphs of two lines are shown.
Graph 1 titled 'Line A' has the intersecting points at (0, 7) and (2, 1). Graph 2 titled 'Line B' has the intersecting points at (0, 0) and (3, 7).
Drag the correct equation for each line to the appropriate box.
Line A
Line B
y=3/7x
y = - 3/7x
y = 7/3x
y = - 7/3x
y = 3x
y = -3x
y = 7x
y = -7x
y = 3x + 7
y = -3x + 7
y = 7x + 3
y = -7x + 3
For Line A: The equation that represents Line A is y = -3x + 7.
For Line B: The equation that represents Line B is y = 7/3x + 0 (or simply y = 7/3x).
Are you sure
Apologies for the confusion earlier. Let's re-address the equations for Line A and Line B.
Line A:
Given intersecting points: (0, 7) and (2, 1)
Using the slope formula, the slope of Line A (m) is:
m = (y2 - y1)/(x2 - x1) = (1 - 7)/(2 - 0) = -6/2 = -3
We can use the point-slope form of a linear equation to find the equation of Line A:
y - y1 = m(x - x1)
y - 7 = -3(x - 0)
y - 7 = -3x
y = -3x + 7
So, the equation of Line A is y = -3x + 7.
Line B:
Given intersecting points: (0, 0) and (3, 7)
Using the slope formula, the slope of Line B (m) is:
m = (y2 - y1)/(x2 - x1) = (7 - 0)/(3 - 0) = 7/3
We can use the point-slope form of a linear equation to find the equation of Line B:
y - y1 = m(x - x1)
y - 0 = 7/3(x - 0)
y = 7/3x
So, the equation of Line B is y = 7/3x.
Apologies for any confusion caused earlier.
Which equations have infinitely many solutions? Select TWO that apply.
A. 6(x - 9) = 6x - 54 + x
B. 5 (x - 8) + 10 = 5(x + 2)
C. 20 - 8x - 6 = 2(7 - 4x)
D. 4(x + 4) = 2(2x + 5) + 6
E. 2x + 9 = 18 + 2x
The equations A and E have infinitely many solutions because they are identities, meaning both sides of the equation are equal for all values of x.
A. 6(x - 9) = 6x - 54 + x simplifies to 6x - 54 = 6x - 54, which is always true.
E. 2x + 9 = 18 + 2x simplifies to 2x + 9 = 2x + 18, and when we subtract 2x from both sides, we get 9 = 18, which is false.
Therefore, the correct answers are A and E.