A line has a slope of 6 and an x-intercept of 7.

Yes, enough information is provided to write the equation of this line. This can be done by using the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 6 and the point is (-1, -1), so the equation is y - (-1) = 6(x - (-1)), which simplifies to y = 6x + 7.

Not quite!

First of all in the original, which is not a question but merely a statement,
it said:
for y = 6x + 7
"the slope is 6 and the x-intercept is 7, so the equation is y = 6x + 7."
That should be the y-intercept is 7, not the x-intercept

secondly, a line parallel to y = 6x + 7 and passing through (-1,-1)
should only differ in the constant
so we start with y = 6x + b , but (-1,-1) lies on it, so
-1 = 6(-1) + b
b = 5

y = 6x + 5

or , the way the bot did it
y+1 = 6(x+1)
y = 6x + 6 - 1
y = 6x + 5

In order to write the equation of a line, we need both the slope and a point on the line. In this case, the same slope of 6 is provided, but we are also given a point (-1, -1). With this additional information, we can now write the equation of the line.

To find the equation, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (-1, -1) for (x1, y1) and 6 for m, we get:

y - (-1) = 6(x - (-1))
y + 1 = 6(x + 1)

Simplifying further:

y + 1 = 6x + 6

Finally, we can write the equation in slope-intercept form by isolating y:

y = 6x + 6 - 1
y = 6x + 5

Therefore, the equation of the line passing through the point (-1, -1) with the slope of 6 is y = 6x + 5.

To determine if enough information is provided to write the equation of the second line, we need to check if we have the slope and a point on the line. In this case, we are given the slope (6) but only have one point (-1, -1).

To find the equation of the second line, we can use the point-slope form of a line equation, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope.

Plugging in the values we have, we get:

y - (-1) = 6(x - (-1))
y + 1 = 6(x + 1)

Now, we can simplify this equation:

y + 1 = 6x + 6

To write the equation in slope-intercept form, y = mx + b, we can rearrange the equation:

y = 6x + 6 - 1
y = 6x + 5

Therefore, the equation of the second line with the same slope as the first and passing through the point (-1, -1) is y = 6x + 5.