Find slope of line, two points on the line are included

[rcmango]

Homework Statement

find the slope of this line it contains these points:

(-16, -1) , (-17, -7)

Homework Equations

y = mx + b

The Attempt at a Solution

i got y = 3/8x - .625

is that correct?

my work i use -7 +1 / -17 + 1

==-6/16


==6/16 = 3/8

then i used -7 = 3/8 * -17 + b

=6.375

 

[Mentallic]

Homework Statement

find the slope of this line it contains these points:

(-16, -1) , (-17, -7)

Homework Equations

y = mx + b

The Attempt at a Solution

i got y = 3/8x - .625

is that correct?

my work i use -7 +1 / -17 + 1

==-6/16


==6/16 = 3/8

then i used -7 = 3/8 * -17 + b

=6.375

Not quite, you got the gradient wrong. In the formula

$$m=\frac{y_2-y_1}{x_2-x_1}$$

You mistakenly substituted y₁ a second time where x₁ is instead meant to be.

Also, your technique to find the missing value of b works, but you might also be interested to know that there is a formula for a line that has gradient m and passes through the point (x₀,y₀) as

$$y-y_0=m(x-x_0)$$

And if we divide both sides by x-x₀, you may see it is quite similar to the gradient formula:

$$m=\frac{y-y_0}{x-x_0}$$

 

[rcmango]

thankyou upon checking my work, i got the m = 6

and the b = 95

and I also used the new point slope formula, thanks.