Question

Which equation represents a line that has a slope of -1/2 and goes through the point (8, 1)

Answer 1

The equation is :

↬ y = -1/2x + 5

Solution:

Let's write the equation in point slope first.

Point slope

The formula is
`\bf{y-y_1=m(x-x_1)}`.

Where

• m = slope
• (x₁, y₁) is a point on the line

Substitute all the data:

`\begin{gathered}\bf{y-1=-(1)/(2)(x-8)}\\\bf{y-1=-(1)/(2) x+4}\\\bf{y=-(1)/(2)x+5}\end{gathered}`

Hence, the answer is y = -1/2x + 5

Answer 2

y = -
`(1)/(2)` x + 5

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given slope m = -
`(1)/(2)` , then

y = -
`(1)/(2)` x + c ← is the partial equation

to find c substitute (8, 1 ) into the partial equation

1 = -
`(1)/(2)` (8) + c = - 4 + c ( add 4 to both sides )

5 = c

y = -
`(1)/(2)` x + 5 ← equation of line