Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept form. ​(−3​,5​), ​(3​,3​)

Answer 1

Hi Isaac!

We can calculate the slope by doing (y2-y1) / (x2-x1).

With our given points ​(−3 "x₁​",5​ "y₁") and ​(3 "x₂"​,3 "y₂​") the equation is going to be (3 - 5) / (3 + 3), which gives us -2 / 6 and can be further broken down into -1 / 3.

Now that we know our slope is (-1 / 3) we can move on to doing the point-slope and the slope-intercept form.

Point-slope form is y−y₁=m(x−x₁).

y - 5 = -1 /3 (x + 3) <-This is the point slop form of the given points.

Slope-intercept form is y = mx + b. (m = slope and b = y-axis point

5 = -1 / 3x (-3) + b

5 = 3 / 3 + b

5 = 1 + b

5 - 1 = 0 + b

b = 4

The slope intercept form is y = - 1 / 3x + 4