Question

Determine the equation of each line.

B.) slope of 1/2, through (4,-4)

Answer 1

The answer is:

`\rm{y=(1)/(2) x-6}`

Work/explanation:

Given the slope and a point on the line, we can write the equation in point slope form, which is:

`\rm{y-y_1=m(x-x_1)}`

Where m is the slope and (x₁, y₁).

Plug the data in the formula:

`\rm{y-(-4)=(1)/(2)(x-4)}`

Simplify:

`\rm{y+4=(1)/(2) (x-4)}`

Now focus on the right side & simplify it :

`\rm{y+4=(1)/(2)x-2}`

Finally, subtract 4 on each side:

`\rm{y=(1)/(2) x-2-4}`

Simplify:

`\rm{y=(1)/(2) x-6}`

This is our equation in slope intercept form.

Therefore, the answer is y = 1/2x - 6.

Answer 2

y = 1/2 x - 6

Explanation:

y = mx + b

y = (1/2)x + b

-4 = (1/2) × 4 + b

-4 = 2 + b

b = -6

y = 1/2 x - 6