To find a solution that satisfies both equations, we need to find the point where the two lines intersect.
The equations of the two lines can be determined using the two given points.
For line one:
First find the slope:
slope = (change in y) / (change in x)
slope = (-4 - 6) / (5 - 1)
slope = -10 / 4
slope = -5/2
Using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is a point on the line
y - 6 = (-5/2)(x - 1)
y - 6 = (-5/2)x + 5/2
y = (-5/2)x + 17/2
y = (-5/2)x + 8.5
For line two:
First find the slope:
slope = (5 -(-5)) / (8 - (-7))
slope = 10 / 15
slope = 2/3
Using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is a point on the line
y + 5 = (2/3)(x + 7)
y + 5 = (2/3)x + 14/3
y = (2/3)x + 14/3 - 15/3
y = (2/3)x - 1/3
Now, we need to find the point of intersection between the two lines:
(-5/2)x + 8.5 = (2/3)x - 1/3
(2/3)x + (5/2)x = 8.5 + 1/3
(11/6)x = 25/3
x = 25/3 * 6 / 11
x = 50 / 11
x = 4.545
Substitute x back into one of the equations to find y:
y = (2/3)(4.545) - 1/3
y = 3.03 - 1/3
y = 3.03 - 0.33
y = 2.7
Therefore, the point of intersection between the two lines is approximately (4.545, 2.7).
None of the given answer choices perfectly match this point, so we can conclude that there is no exact solution given by the answer choices.
the two lines graphed on the coordinate grid each represent an equation.
line one: (1,6) (5,-4)
line two: (-7,-5) (8,5)
which ordered pair represents a solution both equations?
a (1,2)
b (2,1)
c no solution
d (2,2)
1 answer
1 answer