Question

Find an equation of the line having the given slope and containing the given point.

Slope is -2
Line through (5, -6)

Answer 1

y = -2x + 4

Explanation:

Pre-Solving

We are given that a line has a slope (m) of -2 and passes through (5, -6).

We want to write the equation of the line.

There are three ways to write the equation of the line:

• Slope-intercept form, which is y=mx+b, where m is the slope and b the value of y at the y-intercept.
• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
• 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.

Any of these forms will work, however let's put it into slope-intercept form as that is the most common way.

Solving

As we are already given the slope, we can immediately plug that into the equation.

Substitute m with -2.

y = -2x + b

Now, we need to solve for b.

As the equation passes through (5, -6), we can use its values to help solve for b.

Substitute 5 as x and -6 as y.

-6 = -2(5) + b

Multiply.

-6 = -10 + b

Add 10 to both sides.

4 = b

Substitute 4 as b.

y = -2x + 4