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To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula. Use the slope and a given point to substitute for and in the point-slope form, which is derived from the slope equation. Simplify the equation and keep it in point-slope form.


Equation of a Line Parallel and/or Perpendicular to Another Line. In this tutorial, you will learn how to construct a line that is either parallel or perpendicular to a given reference line and passing through a fixed point. To be successful in solving this kind of problem, you need to have some background knowledge about line itself.


When considered as a linear equation in one variable, this equation simply gives us one (unique) solution for x, which is \(x = - 2\). We can represent the solution on a (one-dimensional) number line as a single point: II. However, when considered as a linear equation in two-variables, this represents a line parallel to the y-axis, as shown below:


You must know the structure of a straight-line equation before you can write equations for parallel or perpendicular lines. The standard form of the equation is "y = mx + b," in which "m" is the slope of the line and "b" is the point where the line crosses the y-axis.


The answer is an equation, in slope intercept form, of the line parallel to the line and passing through the point entered. The coordinates and coeficients may be entered as fractions, integers or decimals.(see examples below).


Equation of a Line passing through a point and parallel to a vector Let us consider that the position vector of the given point be \(\vec{a} \) with respect to the origin. The line passing through point A is given by l and it is parallel to the vector \(\vec{k} \) as shown below.


Given equation of line is: 2x+5y=10. We have to convert it into point-slope form. The co-efficient of x is the slope of the line. So, As the required line is parallel to given line, it will also have same slope. Let m1 be the slope of required line. Then the line will be: Putting the value of slope. Putting (-5,1) in the equation to find the ...


Now recall that in the parametric form of the line the numbers multiplied by \(t\) are the components of the vector that is parallel to the line. Therefore, the vector, \[\vec v = \left\langle {3,12, - 1} \right\rangle \] is parallel to the given line and so must also be parallel to the new line. The equation of new line is then,


Explanation: . In order for two lines to be parellel, their slopes have to be the same. Find the slope of the line connecting those two points using the general slope formula, , where the points are and .. In our case, the points are (–8,9) and (3,–4).


Find the slope of the given line. Let. we know that. the formula to calculate the slope is equal to. substitute the values. Step 2. Find the equation of the line. we know that. the equation of the line into point slope form is equal to. we have-----> the x-intercept of the line-----> because parallel line has the same slope. substitute the ...