Question

Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept form. ​(​-9,7​), ​(6​,​2)

Answer 1

The equation in point-slope form is (y - 7) = -1/3(x - (-9)). The equation in slope-intercept form is y = -1/3x + 4.

Step-by-step explanation:

To write the equation in point-slope form, we can use the formula:

(y - y1) = m(x - x1)

where m is the slope and (x1, y1) are the coordinates of one of the points.

Using the points (-9,7) and (6,2), we can calculate the slope:

m = (y2 - y1) / (x2 - x1) = (2 - 7) / (6 - (-9)) = -5 / 15 = -1/3

Now, let's use the point (-9,7):

(y - 7) = -1/3(x - (-9))

Expanding and simplifying the equation, we get:

y - 7 = -1/3x - 3

Finally, let's write the equation in slope-intercept form:

y = -1/3x + 4