Question

How do you write the equation of a line in point slope form that is parallel to `y=7x-1` and goes through (1,-2)?

Answer 1

Point-slope form of an equation for a line is
`(y-y_1) = m(x-x_1)`
for a line with slope `m` through a point `(x_1,y_1)`

Slope (y)intercept form for a line is
`y=mx+b`
for a line with slope `m` and a y-intercept of `b`

The given line `y=7x-1` is in slope-intercept form with a slope of `m=7`

Any line parallel to this will also have a slope of `m=7`

Point-slope form of an equation for a line with `m=7` through the point `(1,-2)` is
`(y-(-2)) = 7(x-1)`
which you might simplify as
`y+2 = 7(x-1)` (although this "hides" the true `y` coordinate value)