write the slope-intercept form of the equation of the line described through (-3,1) parallel to y=-4x-3

Answer 1

The slope-intercept form of a line is y = mx + b, where x and y are coordinates of any point on the line, m is the slope and b is the y-intercept. Parallel lines mean that they have the same slope, therefore, the slope of y = -4x - 3 is the same as the line we are looking for, which is -4.

Knowing a point on the line and the slope we can solve for the y-intercept, b:

y = mx + b

1 = (-4)(-3) + b

1 = 12 + b

b = 1 - 12

b = -11

Now we know m, -4, and b, -11, of the new line. Putting these values back into our general equation of a line in slope-intercept form we get:

y = mx + b

y = -4x - 11 <----your answer!