Question

What is an equation of the line that passes through the points (-6, 1) and (6, 7)?

Answer 1

Answer:y = (1/2)x + 4

Explanation:

The equation of the line that passes through the points (-6, 1) and (6, 7) can be found using the slope-intercept form of a line. The slope m is calculated as (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Plugging in the values for these points gives us a slope of m = (7-1)/(6-(-6)) = 1/2.

Now that we have the slope, we can use point-slope form to find the equation of the line: y - y1 = m(x - x1). Substituting one of our points and our calculated slope into this equation gives us y - 1 = (1/2)(x + 6). Simplifying this expression gives us y = (1/2)x + 4, which is the equation of our line in slope-intercept form.

So, an equation for this line is y = (1/2)x + 4.

Answer 2

y =
`(1)/(2)` x + 4

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (6, 7 )

m =
`(7-1)/(6-(-6))` =
`(6)/(6+6)` =
`(6)/(12)` =
`(1)/(2)` , then

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

to find c substitute either of the 2 points into the partial equation

using (6, 7 )

7 =
`(1)/(2)` (6) + c = 3 + c ( subtract 3 from both sides )

4 = c

y =
`(1)/(2)` x + 4 ← equation of line