Question

Find the equation of the line which passes through the point (-11, 9) and is parallel to a given line express your answer in slope intercept form simplify your answer

Answer 1

Explanation

We must find the equation of the line that:

0. passes through the point (x₀, y₀) = (-11, 9),

,

1. and it is parallel to the line:

$2x+6y=20\Rightarrow6y=-2x+20\Rightarrow y=-\frac{2}{6}x+\frac{20}{6}=-\frac{1}{3}x+\frac{10}{3}.$

(1) The general point-slope equation of a line that passes through a point with coordinates (x₀, y₀) is:

$y=m\cdot(x-x_0)+y_0.$

Where m is the slope.

Replacing the coordinates (x₀, y₀) = (-11, 9), we have:

$y=m\cdot(x-(-11))+9=m\cdot(x+11)+9.$

(2) The general slope-intercept equation of a line is:

$y=m\cdot x+b.$

Comparing this equation with the equation from point 2, we identify the slope:

$m=-\frac{1}{3}.$

The line that passes through (x₀, y₀) = (-11, 9) must have a slope m = -1/3 too because it is parallel to this line. Replacing the value m = -1/3 in the last equation of (1), and then simplifying, we get:

$y=-\frac{1}{3}\cdot(x+11)+9=-\frac{1}{3}x-\frac{11}{3}+9=-\frac{1}{3}x+\frac{16}{3}.$Answer$y=-\frac{1}{3}x+\frac{16}{3}$