Question

what is the equation of the line, in the point-slope form, of a line with a slope of -2/3, which passes through the point (-6,1)

Answer 1

(y – 1) = -⅔(x + 6)

Explanation:

Given:

• Slope of -⅔
• Point/Coordinate of (-6, 1)

To find the point slope form, first use the formula:

(y – y_1) = m(x – x_1).

Where (x_1, y_1) is a given point, and m is the slope of the line.

The next and final step is to substitute the given information into the equation like this.

(y – y_1) = m(x – x_1) →

(y – (1)) = (-⅔)(x – (-6)).

Then simplify:

(y – (1)) = (-⅔)(x – (-6)) → (y – 1) = -⅔(x + 6).

You can also verify that the information is correct if you replace the coordinate for x and y values, so that the equation is true like 0 = 0, or where both sides are the same.

(-6, 1) → (y – 1) = -⅔(x + 6) →

(1 – 1) = -⅔(-6 + 6) → 0 = 0 ✓