Question

Writing Linear Equations

Instruction Active
Writing an Equation Given Two Points on the Line
Write the equation of the line that passes through the points (7,-4) and (-1,3), first in point-slope form, and then in
slope-intercept form.
The slope of the line is
When the point (7.-4) is used, the point-slope form of the line is
The slope-intercept form of the line is

Answer 1

`\text{The slope:}\ m=-(7)/(8)\\\\\text{The point-slope form:}\ y+4=-(7)/(8)(x-7)\\\\\text{The slope-intercept form:}\ y=-(7)/(8)x+(17)/(8)`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

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

We have two points (7, -4) amd (-1, 3).

Calculate the slope:

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

The point-slope form of an equation of a line:

`y-(-4)=-(7)/(8)(x-7)\\\\y+4=-(7)/(8)(x-7)`

Convert to the slope-intercept form:

`y+4=-(7)/(8)(x-7)` use the distributive property

`y+4=-(7)/(8)x+(49)/(8)` subtract 4 = 32/8 from both sides

`y=-(7)/(8)x+(17)/(8)`