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.