Final answer:
Equations that represent the same line as y-11 = 4(x + 7) must have a slope of 4 and pass through the points (-7, 11) and (8, -9). By converting equations to slope-intercept form and comparing their slopes and y-intercepts, and checking whether they pass through the given points, we can determine if they represent the same line.
Step-by-step explanation:
To determine which equations represent the same line as the one given by y-11 = 4(x + 7), we need to find equations that have the same slope and pass through the same points. We can first rewrite the given equation in slope-intercept form (y = mx + b) to make it easier to compare to other equations:
y - 11 = 4(x + 7)
y = 4x + 28 + 11
y = 4x + 39
Now we know that any line with a slope (m) of 4 and y-intercept (b) of 39 will be the same line.
We can use the two given points (-7, 11) and (8, -9) to verify other equations as well. For example, if we plug x = -7 into the equation 7y = 6x + 8, we can see if the resulting y matches one of the points:
7y = 6(-7) + 8
7y = -42 + 8
7y = -34
y = -34/7
y = -4.86
Since -4.86 doesn't match y = 11 when x = -7, the equation 7y = 6x + 8 does not represent the same line. Therefore, we discard this equation.
Following a similar process for each candidate equation, we can find which lines have the slope of 4 and go through the points (-7, 11) and (8, -9). Remember that equations with different slopes or y-intercepts will represent different lines.