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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.


Since the two lines have the same slope and different y y y-intercepts, the two lines are parallel. What is the equation of the line that is parallel to the line 2 x − 3 y − 8 = 0 2x-3y-8=0 2 x − 3 y − 8 = 0 and passes through the point (3, 5)? (3, 5)? (3, 5)?


Parallel Line Formula. The formula for calculating a parallel line is fairly straight forward, as long as you have enough information. You can follow the steps below for calculating the equation of a parallel line.


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.


Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane). Parallel Lines in greater depth. On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 ...


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).


Question 698998: Write an equation of the line that is parallel to the given line and passes through the given point.(I forgot how to solve these, just need a few examples) 1) y = 3 x - 1, (0,2) 2) y = x + 3, (1,2) Thanks Answer by MathLover1(17368) (Show Source):