Write the slope-intercept form of the equation of each line through a given point and parallel/perpendicular to a specific line. through (0, 4) and parallel to y = 1/4x-1

Answer 1

Hi Delanie S

Slope Intercept Form is

y = mx + b where m is the slope and the point with coordinates (0,b) represent the y intercept

Parallel lines have exactly the same slope, and you are actually given the point (0,4) which represents the y intercept for the parallel line so

Since the slope of y = (1/4)x - 1, is 1/4, then the slope of the parallel line has the same slope

y = (1/4)x + b

We were given the y intercept as (0,4) where x = 0 and y = 4 = b; so our parallel line is below

y = (1/4)x + 4

For a line perpendicular to y = (1/4)x -1

A perpendicular line would have a slope m, that is the inverse of 1/4 with opposite sign so m would be

negative 4 (-4/1)

y = -4x + b

Again since we are given the point (0,4) the y intercept we know x = 0, y = 4 = b and finally we have

y = -4x + 4

You can graph all your lines at Desmos.com to check and confirm that they are parallel/perpendicular to y = (1/4)x - 1

Hope this helps.

Answer 2

y = (1/4)x + 4

y = -4x + 4

Do you know how I did that?