Question

How do you find an equation of the line containing the given pair of points (-7, -4) and ( -2, -6)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line running through the two points. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(-6) - color(blue)(-4))/(color(red)(-2) - color(blue)(-7)) = (color(red)(-6) + color(blue)(4))/(color(red)(-2) + color(blue)(7)) = (-2)/5 = -2/5`

We can now use the point-slope formula to write and equation for the line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(red)(-4)) = color(blue)(-2/5)(x - color(red)(-7))`

`(y + color(red)(4)) = color(blue)(-2/5)(x + color(red)(7))`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(red)(-6)) = color(blue)(-2/5)(x - color(red)(-2))`

`(y + color(red)(6)) = color(blue)(-2/5)(x + color(red)(2))`

Answer 2

See the explanation.

Explanation:

First find the slope , `m` of the line, using the two points.

`m=(y_2-y_1)/(x_2-x_1)`

Either point can be 1 or 2. I'm going by the order listed in the question. Point 1`=` `(-7,-4)`, Point 2`=` `(-2,-6)`

Insert the points into the equation.

`m=(-6-(-4))/(-2-(-7))=-2/5`

Now use the point slope form for a straight line.

`y-y_1=m(x-x_1)`

Insert either point as `(x_1,y_1)`. I'm going to use Point 1 from the first part of this answer: `(-4,-7)`.

`y-(-4)=-2/5(x-(-7))`

Simplify.

`y+4=-2/5(x+7)`

`y+4=-2/5x-14`

Solve for `y` to get the slope intercept form for a straight line: `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

Subtract `4` from both sides and simplify.

`y+4=-2/5x-14`

`y=-2/5x-14-4`

`y=-2/5x-18` graph{y=-2/5x-18 [-16.42, 15.6, -25.96, -9.94]}