Question

Find the equation of a line that passes through the points (6,7) and (8,3).

Leave your answer in the form
y = mx + c

Answer 1

y=-2x+19

Explanation:

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form: m=
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`.

Now we have,

m= 3-7/8-6

m=-2. Since m=-2, the equation is y=-2x+b.

To find b, think about what your (x,y) points mean:

(6,7). When x of the line is 6, y of the line must be 7.

(8,3). When x of the line is 8, y of the line must be 3.

Substitute them to the equation y=-2x+b.

You can use either (x,y) point you want..the answer will be the same:

(6,7). y=mx+b or 7=-2 × 6+b, or solving for b: b=7-(-2)(6). b=19.

(8,3). y=mx+b or 3=-2 × 8+b, or solving for b: b=3-(-2)(8). b=19.

So, the equation of the line that passes through the points

(6,7) and (8,3) is y=-2x+19.