Which of the following equations would graph a line parallel to 4y = 7x - x + 8(1 point) Responses
y=3/2x+4
3/2y=x+4
4y=7x+8
y=2x+3
The correct equation that would graph a line parallel to 4y = 7x - x + 8 is:
3/2y = x + 4
To find an equation that would graph a line parallel to 4y = 7x + 8, we need to compare the slopes of the lines. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line.
The given equation, 4y = 7x + 8, can be rearranged in slope-intercept form as y = (7/4)x + 2.
A line is parallel to another line if it has the same slope. So, we need to find an equation with the same slope of (7/4).
Among the options given:
1. y = 3/2x + 4 has a slope of 3/2, which is not equal to 7/4.
2. 3/2y = x + 4 can be rewritten as y = (2/3)x + (8/3), which also has a different slope from 7/4.
3. 4y = 7x + 8 has the same slope as the given equation. Therefore, this equation would graph a line parallel to 4y = 7x + 8.
4. y = 2x + 3 has a slope of 2, which is not equal to 7/4.
So, the correct equation that would graph a line parallel to 4y = 7x + 8 is 4y = 7x + 8.
To determine which equation would graph a line parallel to 4y = 7x - x + 8, we need to analyze the given equation and consider the properties of parallel lines.
The given equation is 4y = 7x - x + 8.
To make it easier to analyze, let's simplify the equation to standard form:
4y = 6x + 8
Divide the equation through by 2, to make the coefficient of x equal to 1:
2y = 3x + 4
Now, to find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope:
y = (3/2)x + 2
From this equation, we can conclude that the slope of the line represented by the original equation (4y = 7x - x + 8) is 3/2.
Parallel lines have the same slope, so we need to find an equation with a slope of 3/2.
Looking at the given options:
A) y = 3/2x + 4
B) 3/2y = x + 4
C) 4y = 7x + 8
D) y = 2x + 3
The equation that has a slope of 3/2 is option A, y = 3/2x + 4.
Therefore, the answer is:
Option A) y = 3/2x + 4