Write an equation of the line that passes through (-5,-1) and is parallel to the line y=4x-6
slope = m = 4
y = 4 x + b
-1 = 4(-5) + b
b = 19
y = 4 x + 19
slope = 4, so the point-slope form of a line is
y+1 = 4(x+5)
massage that into whichever other form you desire
To find the equation of a line that is parallel to another line, we need to know that parallel lines have the same slope. The given line has a slope of 4 (the coefficient of x in y = 4x - 6).
So, our new line will also have a slope of 4.
Now, we have the slope and a point (-5,-1) that lies on the line. We can use the point-slope form of the linear equation to find the equation of the line.
The point-slope form of a linear equation is:
(y - y1) = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the values, we have:
(y - (-1)) = 4(x - (-5))
Simplifying, we get:
(y + 1) = 4(x + 5)
Expanding the equation:
y + 1 = 4x + 20
And rewriting in standard form:
4x - y = 19
So, the equation of the line that passes through (-5,-1) and is parallel to y = 4x - 6 is 4x - y = 19.