Which graph matches the linear equation of 6x+y=-4
The graph of the linear equation 6x+y=-4 is a straight line. Here are the options for the graph:
1. The graph passes through the points (-4, 28) and (0, -4).
2. The graph passes through the points (-2, 8) and (0, -4).
3. The graph passes through the points (-1, -1) and (0, -4).
4. The graph passes through the points (0, -4) and (1, -10).
To determine which graph matches the given equation, we need to substitute the x and y values from each option into the equation and see if it satisfies the equation.
Let's check the options:
1. For option 1, when x = -4 and y = 28:
6(-4) + 28 = -24 + 28 = 4, which is not equal to -4.
2. For option 2, when x = -2 and y = 8:
6(-2) + 8 = -12 + 8 = -4, which is equal to -4.
3. For option 3, when x = -1 and y = -1:
6(-1) + (-1) = -6 - 1 = -7, which is not equal to -4.
4. For option 4, when x = 0 and y = -4:
6(0) - 4 = -4, which is equal to -4.
Therefore, the graph that matches the linear equation 6x+y=-4 is the graph in option 4, which passes through the points (0, -4) and (1, -10).
To determine which graph matches the linear equation 6x + y = -4, 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.
Starting with the equation 6x + y = -4, we isolate y by subtracting 6x from both sides:
y = -6x - 4
Now, we can compare this equation with the slope-intercept form y = mx + b.
From the equation, we can identify that the slope (m) is -6, and the y-intercept (b) is -4.
The graph of a linear equation with a slope of -6 and a y-intercept of -4 will have a downward slope and intersect the y-axis at -4.
Therefore, the correct graph would be a line with a negative slope that crosses the y-axis at -4.
To determine which graph matches the linear equation 6x + y = -4, we first need to rearrange the equation into slope-intercept form, which is y = mx + b. Let's do that:
6x + y = -4
y = -6x - 4
Now the equation is in slope-intercept form, where the coefficient of x (-6 in this case) represents the slope of the line, and the constant term (-4 in this case) represents the y-intercept (the point where the line crosses the y-axis).
Based on this, we can determine that the slope of the line is -6, which means that for each increment of 1 in the x-coordinate, the y-coordinate will decrease by 6 units. The y-intercept is -4, which means that the line intersects the y-axis at the point (0, -4).
Now, let's look at the given graphs and compare them to the equation y = -6x - 4:
Graph A:
If the graph is a straight line that passes through the y-intercept (0, -4) and has a slope of -6, then it matches the equation y = -6x - 4.
Graph B:
If the graph is a straight line that passes through the y-intercept (0, -2) and has a slope of -4, it does not match the equation y = -6x - 4.
Graph C:
If the graph is a straight line that passes through the y-intercept (0, -6) and has a slope of -2, it does not match the equation y = -6x - 4.
Based on this analysis, we can conclude that Graph A matches the linear equation 6x + y = -4.