How do you tell if a line is parallel from an equation?

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel.

How do you tell if a line is perpendicular by the equation?

Perpendicular lines intersect at right angles to one another. To figure out if two equations are perpendicular, take a look at their slopes. The slopes of perpendicular lines are opposite reciprocals of each other.

Do parallel lines have the same equation?

Explanation: Parallel lines have the same slope and differing y-intercepts. Since \displaystyle y = 9x + 5 is the only equation with the same slope, and the y-intercept is different, this is the equation of the parallel line.

Under what conditions are lines perpendicular?

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope. Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

How do you know if the lines are parallel?

If the lines are not parallel, they will intersect exactly once. The only system of equations that consists of parallel lines is the one that consists of the lines 4x – 3y = 2 and 6y = 8x + 9. To determine whether or not these lines are parallel, we need to find their slopes.

How to find perpendicular line with coordinates and line equation?

Perpendicular line is a straight line through a point. It makes an angle of 90 degree with a particular point through which the line passes. Coordinates and line equation is the prerequisite to find out the perpendicular line. Consider the equation of the line is ax + by + c = 0 and coordinates are ( x1, y1 ), the slope should be − ab − ab.

What is the system of lines 4x – 3Y = 2?

If we check all of the other systems of equations, we will find that each consists of lines that aren’t parallel. Thus, all the other choices consist of lines that intersect exactly once. The answer is the system of lines 4x – 3y = 2 and 6y = 8x + 9. Line is given by the equation .

What is the slope of the line 4x – 3Y = 2?

It helps to remember that the slope of a line in the standard form Ax + By = C is equal to -A/B. (Alternatively, you can solve for the slopes by rearranging both lines to slope-intercept form). The line 4x – 3y = 2 is already in standard form, so its slope is -4/-3 = 4/3.