Question

2. A line goes through the points (7,8) and (3, 10).

a) What is the slope of the line?





b) Write the equation of the line in point-slope form. Show your work.






c) Write the equation of the line in slope-intercept form. Show your work.

Answer 1

1.

The formula of a slope (m):

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

We have the points (7, 8) and (3, 10). Substitute:

`m=(10-8)/(3-7)=(2)/(-4)=-(1)/(2)`

2.

a) point-slope form:

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

Substitute:

`y-8=-(1)/(2)(x-7)`

b) slope-intercept form:

`y=mx+b`

`y-8=-(1)/(2)(x-7)\qquad|\text{use distributive property}\\\\y-8=-(1)/(2)x+(7)/(2)\qquad|\text{add 8}=(16)/(2)\ \text{to both sides}\\\\y=-(1)/(2)x+(23)/(2)`