Question

The equation of the line that passes through points (0,-7) and (2,-1) is shown below.What value is missing from the equation?​

Answer 1

The value of missing is 3

Explanation:

* To form an equation of a line from two points on the line, you

must find the slope of the line at first

- The form of the equation is y = mx + c, where m is the slope of the

line and c is the y-intercept

- The rule of the slope of a line passes through point (x1 , y1) and (x2 , y2)

is m = (y2 - y1)/(x2 - x1)

* Lets solve the problem

∵ (0 , -7) and (2 , -1) are tow points on the line

- Let (0 , -7) is the point (x1 , y1) and (2 , -1) is the point (x2 , y2)

∴ m = (-1 - -7)/(2 - 0) = (-1 + 7)/2 = 6/2 = 3

- Lets write the equation

∴ y = 3x + c

- c is the y-intercept means the line intersect the y-axis at point (0 , c)

∵ Point (0 , -7) on the line

∴ The line intersect the y-axis at point (0 , -7)

∴ The y-intercept is -7

∴ The equation of the line is y = 3x - 7

* The value of missing is 3

Answer 2

For this case we have that by definition, the slope-intersection equation of a line is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cutoff point with the y axis

`m = \frac {y2-y1} {x2-x1} = \frac {-1 - (- 7)} {2-0} = \frac {-1 + 7} {2} = \frac {6} { 2} = 3`

Thus, the equation is:

`y = 3x + b`

Substituting a point we find b:
`-7 = 0 + b\\b = -7`

Finally the equation is:

`y = 3x-7`

ANswer:

The missing value is 3