Question

Find the equation of a line that passes through the point (3,1) and has a gradient of -3. Leave your answer in the form y = m x + c

Answer 1

`y = (-3)\, x + 10`.

Explanation:

The question requires that the equation should be in the slope-intercept form
`y = m \, x + c`. The
`m` and
`c` in this equation are constants. In particular:

• 
  `m\!` would represent the slope of this line (also known as the gradient of this line,) whereas
• 
  `c` would be the
  `y`-intercept of this line.

The question states that the slope of this line is
`(-3)`. Therefore,
`m = -3`. Thus, the equation for this line should be in the form
`y = (-3)\, x + c`.

The value of constant
`c` could be found using the other piece of information: the point
`(3,\, 1)` is in this line. In other words, the solution
`\text{$x = 3$ and $y = 1$}` should satisfy the equation
`y = (-3)\, x + c`.

Substitute
`\text{$x = 3$ and $y = 1$}` into the equation
`y = (-3)\, x + c` and solve for
`c`:

`1 = (-3) * 3 + c`.

`1 = -9 + c`.

`c = 10`.

Hence,
`y = (-3) \, x + 10` would be the slope-intercept form of the equation of this line.