Question
What would a line graph look like for the equation -5/2x-1=4x+2
Answers
GPT 3.5
To represent the equation -5/2x - 1 = 4x + 2 in a line graph, we need to rearrange the equation to its standard form, y = mx + b, where y is the dependent variable (the vertical axis), x is the independent variable (the horizontal axis), m is the slope, and b is the y-intercept.
Since the equation -5/2x - 1 = 4x + 2 includes both x and y, we transform it into a linear equation by isolating x on one side and simplifying the other side. Starting with:
-5/2x - 1 = 4x + 2
To simplify the equation, we first add 5/2x to both sides:
-5/2x + 5/2x - 1 = 4x + 5/2x + 2
Simplifying further:
-1 = 13/2x + 2
Next, we subtract 2 from both sides:
-1 - 2 = 13/2x + 2 - 2
Simplifying further:
-3 = 13/2x
To isolate x, we need to divide both sides by 13/2:
-3 / (13/2) = (13/2)x / (13/2)
Simplifying further:
-6/13 = x
Now we have x = -6/13, which represents the slope-intercept form y = mx + b, where m (slope) = -6/13 and b (y-intercept) = 0.
In a line graph, the y-intercept represents the point where the line crosses the y-axis, which in this case is 0. We plot the point (0, 0).
To find additional points to plot, we plug in different x-values in the equation to find the corresponding y-values. For simplicity, we can choose x = 13 as a convenient value since it cancels out the denominator in the slope calculation.
Plugging x = 13 into the equation y = (-5/2)x - 1:
y = (-5/2)(13) - 1
y = -65/2 - 1
y = -65/2 - 2/2
y = -67/2
The point (13, -67/2) can be plotted on the line graph.
Connecting the points (0, 0) and (13, -67/2) with a straight line will represent the graph of the equation -5/2x - 1 = 4x + 2.
Since the equation -5/2x - 1 = 4x + 2 includes both x and y, we transform it into a linear equation by isolating x on one side and simplifying the other side. Starting with:
-5/2x - 1 = 4x + 2
To simplify the equation, we first add 5/2x to both sides:
-5/2x + 5/2x - 1 = 4x + 5/2x + 2
Simplifying further:
-1 = 13/2x + 2
Next, we subtract 2 from both sides:
-1 - 2 = 13/2x + 2 - 2
Simplifying further:
-3 = 13/2x
To isolate x, we need to divide both sides by 13/2:
-3 / (13/2) = (13/2)x / (13/2)
Simplifying further:
-6/13 = x
Now we have x = -6/13, which represents the slope-intercept form y = mx + b, where m (slope) = -6/13 and b (y-intercept) = 0.
In a line graph, the y-intercept represents the point where the line crosses the y-axis, which in this case is 0. We plot the point (0, 0).
To find additional points to plot, we plug in different x-values in the equation to find the corresponding y-values. For simplicity, we can choose x = 13 as a convenient value since it cancels out the denominator in the slope calculation.
Plugging x = 13 into the equation y = (-5/2)x - 1:
y = (-5/2)(13) - 1
y = -65/2 - 1
y = -65/2 - 2/2
y = -67/2
The point (13, -67/2) can be plotted on the line graph.
Connecting the points (0, 0) and (13, -67/2) with a straight line will represent the graph of the equation -5/2x - 1 = 4x + 2.