Question

Find an equation of the line having the given slope and containing the given point. Slope 7 through (6,3)​

Answer 1

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})~\hspace{10em} \stackrel{slope}{m}\implies 7 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{7}(x-\stackrel{x_1}{6}) \\\\\\ y-3=7x-42\implies y = 7x-39`

Answer 2

`y-3=7(x-6)`

Explanation:

Pre-Solving

We are given that a line has a slope (m) of 7 and passes through the point (6,3).

We want to write the equation of this line.

There are three ways to do it:

• Slope-intercept form, which is y=mx+b where m is the slope and b is the value of y at the y-intercept.
• Point-slope form, which is
  `y-y_1=m(x-x_1)` where m is the slope and
  `(x_1,y_1)` is a point.
• Standard form, which is ax+by=c where a, b, and c are free integer coefficients.

As the question doesn't specify, either form should work, but let's write the equation in point-slope form as that's the easiest to do.

Solving

As we are already given both the point and the slope, we can plug them both into the equation.

Starting with the slope, substitute 7 for m.

`y-y_1=7(x-x_1)`

Now, substitute 6 as
`x_1` and 3 as
`y_1`.

`y-3=7(x-6)`