15. Which graph matches the linear equation: −2x+3y=-6
(0,4) (1,-10)
(1,2) (0,-4)
(0,2) (1,-1)
(3,0) (0,-2)
To find the matching graph, we can substitute the given points into the equation and see which choice results in a true statement.
Let's try (0,4):
-2(0) + 3(4) = -6
0 + 12 = -6
12 ≠ -6
Let's try (1,-10):
-2(1) + 3(-10) = -6
-2 - 30 = -6
-32 ≠ -6
Let's try (1,2):
-2(1) + 3(2) = -6
-2 + 6 = -6
4 ≠ -6
Let's try (3,0):
-2(3) + 3(0) = -6
-6 + 0 = -6
-6 = -6
None of the points result in a true statement except for (3,0). Thus, the graph that matches the linear equation -2x + 3y = -6 is (3,0)(0,-2).
To determine which graph matches the linear equation −2x + 3y = -6, we need to substitute the given points into the equation and see which pair satisfies the equation.
Let's start by substituting the values of the first point (0,4) into the equation:
-2(0) + 3(4) = -6
0 + 12 = -6
12 ≠ -6
Next, let's substitute the values of the second point (1,-10) into the equation:
-2(1) + 3(-10) = -6
-2 - 30 = -6
-32 ≠ -6
Next, let's substitute the values of the third point (1,2) into the equation:
-2(1) + 3(2) = -6
-2 + 6 = -6
4 ≠ -6
Finally, let's substitute the values of the fourth point (3,0) into the equation:
-2(3) + 3(0) = -6
-6 + 0 = -6
-6 = -6
Since the fourth point (3,0) satisfies the equation, the graph that matches the linear equation −2x + 3y = -6 is represented by the points (3,0) and (0,-2). Therefore, the answer is (3,0) (0,-2).
To determine which graph matches the linear equation −2x + 3y = -6, we need to find the coordinates (x, y) that satisfy the equation.
Let's go through the given options one by one and substitute the x and y values to check if they satisfy the equation.
Option 1: (0,4)
Substituting x = 0 and y = 4 into the equation, we have:
−2(0) + 3(4) = -6
12 = -6
The equation is not satisfied, so this option is not correct.
Option 2: (1,-10)
Substituting x = 1 and y = -10 into the equation, we have:
−2(1) + 3(-10) = -6
-2 - 30 = -6
-32 = -6
This equation is also not satisfied, so this option is not correct.
Option 3: (1,2)
Substituting x = 1 and y = 2 into the equation, we have:
−2(1) + 3(2) = -6
-2 + 6 = -6
4 = -6
Again, this equation is not satisfied, so this option is not correct.
Option 4: (0,2)
Substituting x = 0 and y = 2 into the equation, we have:
−2(0) + 3(2) = -6
0 + 6 = -6
6 = -6
Once more, this equation is not satisfied, so this option is not correct.
Finally, we have checked all the options and found that none of them satisfy the equation −2x + 3y = -6. Therefore, none of the given graphs matches the linear equation.