what is the equation of a line parallel to the given line and passing though the given point y=x+4 ;(-7, 1)

I need other form

the new line is parallel, so it must differ only by the constant.

new line:
y = x + b
sub in (-7,1) to find b, then rewrite my equation

To find the equation of a line parallel to the given line (y = x + 4) and passing through the given point (-7, 1), we can use the concept of parallel lines.

Two lines are parallel if they have the same slope. The given line has a slope of 1 since it is in the form y = mx + b, where m is the slope. To find a line parallel to this, we need to use the same slope.

So, the slope of the line we want to find is also 1.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Plugging in the values, we get:

y - 1 = 1(x - (-7))

Simplifying, we have:

y - 1 = x + 7

To put it in slope-intercept form (y = mx + b), we can rearrange the equation:

y = x + 8

Therefore, the equation of the line parallel to y = x + 4 and passing through (-7, 1) is y = x + 8.