Question

A line passes through the points (-6, -7) and (-2, 1). The equation of this line can be expressed as y = mx + b, where m and b are integers.

Answer 1

• 
  `m=2`

• 
  `b=5`

Explanation:

As a line passes through the points

• (-6, -7) and

• (-2, 1)

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(-2,\:1\right)`

`m=(1-\left(-7\right))/(-2-\left(-6\right))`

`m=2`

As the equation of the line in slope-intercept form be

`y = mx + b`

Putting the point (-6, -7) and m = 2 in slope-intercept form

`y = mx + b`

`\left(-7\right)=\left(2\right)\left(-6\right)+b`

`-2\cdot \:6+b=\left(-7\right)`

`-12+b=-7`

`b=5`

Therefore,

• 
  `m=2`

• 
  `b=5`