To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.
We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:
y - (-1) = 4(x - (-2))
Simplifying this expression gives us:
y + 1 = 4(x + 2)
Which simplifies to:
y = 4x + 5
So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.