**equation of a line**that

**is parallel**or

**perpendicular to a given line**? Possible answer: The slopes of

**parallel lines**are equal. Substitute the known slope and the coordinates of a

**point**on the other

**line**into the

**point**-slope form to

**find the equation**of the

**parallel line**.

Considering this, how do you write an equation parallel to a given line?

Two **lines** are **parallel** if the have the same slope. **Example** 1: Find the slope of the **line parallel** to the **line** 4x – 5y = 12. To find the slope of this **line** we need to get the **line** into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the **line** 4x – 5y = 12 is m = 4/5.

what is the equation of a perpendicular line? The given **equation** is in standard form, so it must be converted to slope-intercept form: y = mx + b to discover the slope is –2/3. To be **perpendicular** the new slope must be 3/2 (opposite reciprocal of the old slope).

In respect to this, what is the equation of the line that passes through the origin and is parallel to?

The standard form of a line is y=mx +b. since the line we are looking for is parallel to the above that tells us that the slopes are the same. The line whose equation we want goes through the origin which gives a point (0,0) and we know the **slope** m= 2/17.

Are these lines perpendicular?

Explanation: Two **lines** are **perpendicular** if and only if their slopes are negative reciprocals. To find **the** slope, we must put **the** equation into slope-intercept form, , where equals **the** slope of **the line**. Therefore, any **line perpendicular** to must have a slope of .