Question

What is the equation of the line that passes through the point (3,-6) and has a slope of −3?

Answer 1

The equation of the line passes through the point
`(3,-6)` and has a slope
`-3` is
`y=-3x+3`.

What are a line and the slope of a line?

Line:

• A line has only one dimension i.e., length and no width.
• It is formed with an infinite number of points lying on it.
• It can be extended infinitely along a straight path in both directions.
• An infinite number of lines pass through a given point, and a unique straight line can be drawn if any two points on that line are shown.

The slope of a line:

The slope of a line is the tangent value of the angle
`\theta` i.e.,
`\tan \theta`, where
`\theta` is the angle made by the line with the positive
`x`-axis.

Equation of a line:

The equation of a line in slope-intercept form is given by
`y=mx+c`, where
`m` is the slope of the line and
`c` is the
`y` intercept of the line.

Here, we want to find the equation of the line which passes through the point
`(3,-6)` and has a slope
`-3`.

So, put
`m=-3` in
`y=mx+c` and obtain
`y=-3x+c`.

Now, since the line passes through the point
`(3,-6)`, put
`x=3` and
`y=-6` in
`y=-3x+c` to obtain:

`-6=-3* 3+c\\\Longrightarrow -6=-9+c\\\Longrightarrow c=-6+9\\\Longrightarrow c=3`

Therefore, after substituting
`c=3` in
`y=-3x+c`, we obtain the required equation of the line that is
`y=-3x+3`.

So, the equation of the line that passes through the point
`(3,-6)` and has a slope
`-3` is
`y=-3x+3`.