Question

Complete the equation of the line through ( -6 , 5 ) and ( -3 , -3 )

Answer 1

The equation of the line through the points (-6, 5) and (-3, -3) is y = (8/3)x + 21.

Step-by-step explanation:

To find the equation of a line through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b. First, we need to find the slope (m) of the line by using the formula: m = (y2 - y1) / (x2 - x1). For the points (-6, 5) and (-3, -3), the slope is: m = (-3 - 5) / (-3 - (-6)) = 8 / 3. Next, we can substitute one of the points and the slope into the equation y = mx + b to solve for the y-intercept (b). Using the point (-6, 5), we have: 5 = (8/3)(-6) + b. Simplifying this equation, we find: b = 5 + 16 = 21. Therefore, the equation of the line through the points (-6, 5) and (-3, -3) is y = (8/3)x + 21.

Answer 2

`y =  ((8)/(-3))(x) - 16`

Step-by-step explanation:

The given points are (-6,5) and (-3,-3)

The equation of the line is of the form,

`(y-y1) = m(x-x1)` , m is the slope of line and (x1,y1) is one of the end points.

The slope m of the line is calculated as,

`((y2)-(y1))/((x2)-(x1)) = ((5)-(-3))/((-6)-(-3)) = (8)/(-3)`

Thus the line equation is,

`(y-5) =  ((8)/(-3))(x-(-6))`

`y =  ((8)/(-3))(x-(-6)) + 5`

`y =  ((8)/(-3))(x) - 16`