Question

Write an equation of the line that passes through each pair of points (5, 7), (-8, -4)

Answer 1

y = 11x/13 + 36/13

Explanation:

We can write the line using y = mx + b form.

To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):

(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.

To find b, we can plug in one of the points. Lets use (5, 7).

y = 11/13 * x + b

7 = 11/13 * 5 + b

7 - 55/13 = b

b = 91/13 - 55/13 = (91-55)/13 = 36/13.

Your equation is:

y = 11x/13 + 36/13.

Answer 2

Answer: y =
`(11)/(13)`x +
`(36)/(13)`

Explanation:

First, we will find the slope.

`m=\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) )=(-4-7)/(-8-5) =(-11)/(-13) =(11)/(13)`

Next, we will substitute this slope and a given point in and solve for our y-intercept (b).

y =
`(11)/(13)`x + b

(7) =
`(11)/(13)`(5) + b

(7) =
`(11)/(13)`(5) + b

7 =
`(55)/(13)` + b

b = 7 -
`(55)/(13)`

b =
`(36)/(13)`

Final equation:

y = mx + b

y =
`(11)/(13)`x +
`(36)/(13)`