which of the following equations has a graph that is parallel to the graph of 4x-2y=7?
1)4x+2y=2
2)-2y=4x+2
3)7-4x=2y
4)2y=4x+7
5)-4x-2y=-7
Enter the slope of a line perpendicular to the line whose equation is 3y-5x=15
To determine which equation has a graph that is parallel to the graph of 4x - 2y = 7, we need to compare the slopes of the equations.
The given equation is in the form of Ax + By = C. The slope-intercept form is y = mx + b, where m represents the slope. To find the slope in the slope-intercept form, we need to rearrange the given equation:
4x - 2y = 7
-2y = -4x + 7
y = (4/2)x - 7/2
y = 2x - 7/2
From this equation, we can determine that the slope is 2.
Now let's evaluate the slopes of the options given one by one:
1) 4x + 2y = 2 (putting in slope-intercept form)
2y = -4x + 2
y = -2x + 1/2
The slope of this equation is -2, which is not parallel to the given equation.
2) -2y = 4x + 2 (putting in slope-intercept form)
2y = -4x - 2
y = -2x - 1
The slope of this equation is -2, which is parallel to the given equation.
3) 7 - 4x = 2y (putting in slope-intercept form)
2y = -4x + 7
y = -2x + 7/2
The slope of this equation is -2, which is parallel to the given equation.
4) 2y = 4x + 7 (putting in slope-intercept form)
y = 2x + 7/2
The slope of this equation is 2, which is not parallel to the given equation.
5) -4x - 2y = -7 (putting in slope-intercept form)
-2y = 4x - 7
y = -2x + 7/2
The slope of this equation is -2, which is parallel to the given equation.
So, the equations that are parallel to the graph of 4x - 2y = 7 are options 2), 3), and 5).
To determine which equation has a graph that is parallel to the graph of 4x - 2y = 7, we need to compare the coefficients of x and y in each equation.
The equation 4x - 2y = 7 is in standard form, where the coefficient of x is 4 and the coefficient of y is -2.
Now, let's compare the coefficients of x and y in each given equation:
1) 4x + 2y = 2
Coefficient of x: 4; Coefficient of y: 2
Since the coefficient of x is the same as in the original equation, this equation is not parallel.
2) -2y = 4x + 2
Coefficient of x: 4; Coefficient of y: -2
Similarly, this equation is not parallel because the coefficient of x is the same but the coefficient of y is different.
3) 7 - 4x = 2y
Coefficient of x: -4; Coefficient of y: 2
Finally, we have an equation where the coefficient of y matches the original equation (-2). Thus, this equation is parallel to the graph of 4x - 2y = 7.
4) 2y = 4x + 7
Coefficient of x: 4; Coefficient of y: 2
This equation is not parallel since the coefficient of y is different from the original equation.
5) -4x - 2y = -7
Coefficient of x: -4; Coefficient of y: -2
Once again, the coefficients of both x and y are different from the original equation, so this equation is not parallel.
Therefore, the correct answer is option 3) 7 - 4x = 2y, as it has a graph parallel to the graph of 4x - 2y = 7.
After re-arranging
1) 2) 3) and 5) all would start with 4x + 2y ...
so clearly they cannot be parallel to 4x - 2y ....
4) ----> 0 = 4x - 2y + 7
ahhhh, that's the one !