General equation of a line

Question

part 1: Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work in your final answer. 

 

part 2:Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer

Answer 1

Find  the slope of the line:

 

2x + y = -5

 

y = -2x - 5, the slope is -2, so with a y-int of 2 we get:

 

y = -2x + 2

 

The second slope is -1, equation is y=-x

Answer 2

part 1: Write the equation of the line, in standard form,

that has a y-intercept of 2 and is parallel to 2x + y = -5.

 

Parallel lines have the same slope.

Your initial equation can be rewritten as y = -2x-5

which has a slope of -2.

You want a line with slope m=-2 and y-intercept (0,b) of 2.

 

y = -2x + 2

In standard form this is 2x + y = 2

 

part 2:Write the equation of the line, in standard form,

that passes through the origin and is parallel to x + y = 6.

 

x + y = 6

y = -x + 6

Slope; m = -1

You want a line with slope m = -1 thru point (0,0)

Using the point slope form: y - y₁ = m(x-x₁)

where m= slope = -1 and point (x₁, y₁) is on the line:

 

y - 0 = -1(x-0)

y = -x

 

In standard form this is

 

x + y = 0