Question

Complete the equation of the line through (-10, -7) and (-5, -9), please

Answer 1

y =
`(-2)/(5)` x - 3

Explanation:

The slope intercept form of a line is

y = mx + b The m is the slope and the b is the y-intercept. We will use the points given to find the m and the b.

Slope (m):

The slope is the change in y over the change in x.

(-10,-7) (-5,-9) The first number in the ordered pair is the x values and the second number is the y values.

The y's are -9 and -7.

The x's are -5 and -10

`(-9-(-7))/(-5-(-10))` =
`(-9 + 7)/(-5 + 10)` =
`(-2)/(5)`

The slope (m) is
`(-2)/(5)`

y-intercept:

To find the y-intercept we need a point on the line and the slope (m). We are given 2 points on the line. It does not matter which point you use. I am going to use (-10,-7).

We will use -10 for x from the point.

We will use -7 for y from the point.

We will use the slope (m) that we just calculated
`(-2)/(5)`

y = mx + b Substitute in all that we know and then solve for b

-7 = (
`(-2)/(5)`)(-10) + b

-7 =
`(-2)/(5)` ·
`(-10)/(1)` + b

-7 =
`(-20)/(5)` + b

-7 = -4 + b Add 4 to both sides

-7 + 4 = -4 + 4 + b

-3 = b

The y-intercept is -3.

Now that we have the slope (m)
`(-2)/(5)` and the y-intercept (b) of -3, we can write the equation

y = mx + b

y =
`(-2)/(5)` x -3

Helping in the name of Jesus.

Answer 2

`y = mx + b`

we should find m(slope) and use this equation y-y1=m(x-x1)

`m = (y2 - y1)/(x2 - x1) \\ m = ( - 9 - ( - 7))/( - 5 - ( - 10)) \\ m= ( - 9 + 7)/( - 5 + 10) \\m = ( - 2)/(5)`

`y - y1 = m(x - x1) \\ y - ( - 7) = ( - 2)/(5) (x - ( - 10)) \\ y + 7 = ( - 2)/(5) (x + 10) \\ y + 7 = ( - 2)/(5) x - 4 \\ y = ( - 2)/(5) x - 4 - 7 \\ y = ( - 2)/(5) x - 11`