Question

Write an equation in slope-intercept form for the following line:

(-17,-4) and (-7,-13)

Answer 1

Slope-intercept form

Linear equations are often organized in slope-intercept form:

`y=mx+b`

• (x,y) = a point that falls on the line
• m = the slope of the line
• b = the y-intercept of the line

Slope (m)

The slope of a line is equal to its
`(rise)/(run)`.

• "Rise" refers to the number of units the line travels up.
• "Run" refers to the number of units the line travels to the right.

Typically, we would solve for the slope by using the following formula:

• 
  `m=(y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
  `(x_1,y_1)` and
  `(x_2,y_2)`

Y-intercept (b)

The y-intercept of a line refers to the y-value that occurs when x=0.

On a graph, it is the y-value where the line crosses the y-axis.

Writing the Equation

1) Determine the slope of the line (m)

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

Plug in the two given points, (-17,-4) and (-7,-13):

`m=(-13-(-4))/((-7)-(-17))\\\\m=(-13+4)/(-7+17)\\\\m=(-9)/(10)`

Therefore, the slope of the line is
`-(9)/(10)`. Plug this into
`y=mx+b`:

`y=-(9)/(10)x+b`

2) Determining the y-intercept (b)

`y=-(9)/(10)x+b`

Plug in one of the given points and solve for b:

`-4=-(9)/(10)(-17)+b\\\\-4=(153)/(10)+b\\\\b=-(193)/(10)`

Therefore, the y-intercept of the line is
`-(193)/(10)`. Plug this back into our equation:

`y=-(9)/(10)x-(193)/(10)`

Answer

`y=-(9)/(10)x-(193)/(10)`