Question

1. Write the equation of the line passing
through the point (2, -1) with a slope of -3.

Answer 1

Equation of the line in slope-intercept form:
`y = -3\, x + 5`.

Explanation:

Consider the point-slope equation of a line. If
`m` is the slope of the line and
`(x_0,\, y_0)` is a point on the line, then the equation of the line will be:

`\displaystyle (y - y_0)/(x - x_0) = m`.

In this question,

• 
  `m= -3`,
• 
  `x_0 = 2`,
• 
  `y_0 = -1`.

The point-slope equation for this line will be:

`\displaystyle (y - (-1))/(x - 2) = -3`.

Simplify to get:

`y - (-1) = (-3) \, (x - 2)`.

`y + 1 = -3\, x + 6`.

`y = -3\, x + 5`.