Question 1204094

write an equation in slope intercept form for the line that passes through (0,5) and is parallel to the line whose equation is 4x-y=3

parallel lines have the same slope.

4x-y =3 is the equation of given line

The equation of line in slope intercept fprm is y= mx+c where m is the slope and c is the y intercept

Write in slope intercept form

y= 4x-3

comparing with y= mx+c 
m=4

The line  passes through (0,5) and slope 4

Use the point-slope form of a linear equation to find the equation of the new line:

y - y₁ = m(x - x₁) where m is the slope and (x1,y1) is the point

{{{ (y-5)= 4(x-0)}}}

y-5=4x

y=4x+5

The equation of the line that is parallel to 4x - y = 3 and passing through (0, 5) in slope-intercept form is:

y = 4x + 5