Find parametric equations of the line of intersection of the two planes 7x+8y = -1 and -9x-7y+4z = -7.
What is the direction vector used?
Parametric equations of a line are a way of representing a line in two-dimensional space using two variables, typically denoted as x and y. These equations express the coordinates of any point on the line as functions of a third variable, usually denoted as t.
Parametric equations use a third variable to represent the coordinates of points on a line, while slope-intercept form uses the slope and y-intercept of a line. Parametric equations are also more flexible and can represent lines in any orientation, while slope-intercept form is limited to lines that are either horizontal or vertical.
To convert parametric equations to slope-intercept form, you can eliminate the third variable by solving for t in terms of x or y. This will give you an equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Parametric equations are used in many fields, including physics, engineering, and computer graphics. They are often used to model the motion of objects in space, such as the trajectory of a projectile, or the position of a point on a moving object. They are also used in computer graphics to create smooth and realistic animations.
To graph parametric equations, you can first choose a range of values for the third variable, t. Then, plug these values into the parametric equations to find the corresponding x and y coordinates. Plot these points on a graph and connect them to create the line. Alternatively, you can use a graphing calculator or online graphing tool to automatically plot the line for you.