Use the given conditions to write an equation for the line i

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form Passing through (-2. -2) and parallel to the line whose equation is y = - 3x + 3 Write an equation for the line in point-slope form (Simplify your answer Use integers or tractions for any numbers in the equation) Write an equation for the line m slope intercept form (Simplify your answer Use integers oi fractions for any numbers in the equation 1 Enter your answer in each at the answer boxes ______________________

Solution

y=-3x+3 the given equation can be written as 3x+y-3=0.(1)

any equation parallel to (1) can be written as 3x+y+k=0. since it passes through (-2,-2)

we get 3(-2)+(-2)+k=0 and therefore -6-2+k=0 implies k=8

the given equation is written as 3x+y+8=0 (2)

slope-point form is passing through (-2,-2)

differentiate (2) we get 3+dy/dx=0 and dy/dx=-3

slope point form is y-y1=dy/dx(x-x1)

y-(-2)=-3(x-(-2) implies y+2=-3(x+2)

y+2=-3x-6 implies 3x+y=-8

slope intercept form of 3x+y+8=0   is y=-3x-8