13. Which graph matches the linear equation: 6x+y=−4
(1 point)
Responses
(0,2) (1,-1)
(3,0) (0,-2)
(0,-4) (1,-10)
(1,2) (0,-4)
To find which graph matches the linear equation 6x + y = -4, we can plug in the coordinates from each graph into the equation and see which one satisfies it.
Let's check each option:
(0,2):
6(0) + 2 = 0 + 2 = 2 ≠ -4
This option does not satisfy the equation.
(1,-1):
6(1) + (-1) = 6 - 1 = 5 ≠ -4
This option does not satisfy the equation.
(3,0):
6(3) + 0 = 18 + 0 = 18 ≠ -4
This option does not satisfy the equation.
(0,-2):
6(0) + (-2) = 0 - 2 = -2 ≠ -4
This option does not satisfy the equation.
(0,-4):
6(0) + (-4) = 0 - 4 = -4
This option satisfies the equation because the left side equals the right side.
(1,2):
6(1) + 2 = 6 + 2 = 8 ≠ -4
This option does not satisfy the equation.
The only option that satisfies the equation is (0,-4), so the graph that matches the linear equation 6x + y = -4 is the one with the coordinates (0,-4).
To determine which graph matches the linear equation 6x + y = -4, we need to find two points that satisfy this equation and are represented on one of the graphs.
Let's find two points that satisfy the given equation:
To find the x-coordinate for the first point, we can set y = 0 and solve for x:
6x + 0 = -4
6x = -4
x = -4/6
x = -2/3
So, the first point is (-2/3, 0).
For the second point, let's choose x = 0 and solve for y:
6(0) + y = -4
y = -4
So, the second point is (0, -4).
Now, let's check which graph includes these two points:
- (0, 2) (1, -1): These points do not satisfy the equation.
- (3, 0) (0, -2): These points do not satisfy the equation.
- (0, -4) (1, -10): (0, -4) satisfies the equation, but (1, -10) does not.
- (1, 2) (0, -4): These points do not satisfy the equation.
Therefore, the graph that matches the linear equation 6x + y = -4 is (0, -4) (1, -10).
To determine which graph matches the linear equation, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Given equation: 6x + y = -4
Rearranging the equation, we get:
y = -6x - 4
Now we can see that the slope (m) is -6 and the y-intercept (b) is -4.
Looking at the given options, we can determine the correct graph by checking if the slope and y-intercept match.
Let's go through each option:
Option 1: (0,2) (1,-1)
The slope is not -6, so this graph does not match the equation.
Option 2: (3,0) (0,-2)
The slope is not -6, so this graph does not match the equation.
Option 3: (0,-4) (1,-10)
The slope is not -6, so this graph does not match the equation.
Option 4: (1,2) (0,-4)
The slope is -6, which matches the equation, and the y-intercept is -4, which also matches the equation.
Therefore, the correct graph that matches the linear equation is Option 4: (1,2) (0,-4).