Answer to Question #232492 in Analytic Geometry for Max

Question

Find the equation of a straight line which oases through the point (2,-3) and is parallel to the line 2x + y = 6.

Answer 1

The equation of the line $2x + y = 6$ in slope-intercept form is

$$y=-2x+6$$

Hence

$$slope=m=-2$$

Then the equation of a line which is parallel to the line $y=-2x+6$ is

$$y=-2x+b$$

If the line passes through the point $(2, -3),$ then

$$-3=-2(2)+b$$

Solve for $b$

$$b=1$$

Then the equation of a line which is parallel to the line $2x + y = 6$ and passes through the point $(2, -3)$ is

$$y=-2x+1$$

Or

$$2x+y=1$$