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- Check their y-intercepts (where they cross the y-axis) as well as their slope: Example: is y = 3x + 2 parallel to y − 2 = 3x ? For y = 3x + 2: the slope is 3, and y-intercept is 2 For y − 2 = 3x: the slope is 3, and y-intercept is 2 So they are the same line and so are not parallel
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How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2.
- Slope
- −0.5
Sep 12, 2020 · Two curves are parallel if at any point you draw a line perpendicular to the tangent line and passes through the point of tangency (the normal line), the normal lines are all parallel, at any point along the curve, and the distance between the line's points of intersections with the two curves are all the same.
Dec 29, 2020 · If a curve is not smooth at \(t=t_0\), it means that \(x^\prime(t_0)=y^{\prime}(t_0)=0\) as defined. This, in turn, means that rate of change of \(x\) (and \(y\)) is 0; that is, at that instant, neither \(x\) nor \(y\) is changing. If the parametric equations describe the path of some object, this means the object is at rest at \(t_0\).
Find the equations of parallel and perpendicular lines. Write the equations of lines that are parallel or perpendicular to a given line. Parallel lines have the same slope and different y- intercepts.
Jul 5, 2023 · In this section we will introduce parametric equations and parametric curves (i.e. graphs of parametric equations). We will graph several sets of parametric equations and discuss how to eliminate the parameter to get an algebraic equation which will often help with the graphing process.
Aug 24, 2022 · Parallel lines have the same slope; Perpendicular lines have negative reciprocal slopes; How to find an equation of a line parallel to a given line. Find the slope of the given line. Find the slope of the parallel line. Identify the point. Substitute the values into the point-slope form: \(y−y_1=m(x−x_1)\). Write the equation in slope ...
Jul 22, 2021 · Given the equations of two lines, determine whether their graphs are parallel or perpendicular. Write the equation of a line parallel or perpendicular to a given line. Solve a system of linear equations. Two competing telephone companies offer different payment plans.
