Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:



Answer to a math question Determine the general equation of the straight line that passes through the point P (2;-3) and is parallel to the straight line with the equation 5x – 2y 1 = 0:

Expert avatar
34 Answers
To find the equation of a line parallel to \(5x - 2y + 1 = 0\) and passing through point \(P(2, -3)\), we need to determine the slope of the given line first. The equation \(5x - 2y + 1 = 0\) can be rewritten in the slope-intercept form \(y = mx + c\) by rearranging it: \[5x - 2y + 1 = 0\] \[2y = 5x + 1\] \[y = \frac{5}{2}x + \frac{1}{2}\] From this form, we see that the slope of the line is \(m = \frac{5}{2}\). A line parallel to this line will have the same slope. So, the slope (\(m\)) of the line we're looking for is also \(m = \frac{5}{2}\). Now that we have the slope and the point \(P(2, -3)\), we can use the point-slope form of the equation of a line: \[y - y_1 = m(x - x_1)\] Substitute $4\(x_1 = 2\), \(y_1 = -3\), and \(m = \frac{5}{2}\)$$: \[y - (-3) = \frac{5}{2}(x - 2)\] \[y + 3 = \frac{5}{2}x - 5\] \[y = \frac{5}{2}x - 5 - 3\] \[y = \frac{5}{2}x - 8\] Therefore, the general equation of the straight line passing through point \(P(2, -3)\) and parallel to the line \(5x - 2y + 1 = 0\) is \(y = \frac{5}{2}x - 8\).

Frequently asked questions (FAQs)
What is the integral of 2x^3 + 5x^2 - 3x + 1 with respect to x?
Find the value of x such that the reciprocal function f(x) = 1/x equals its own inverse.
What is the result of multiplying 25 by 8 and then adding 17?
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
A=m/2-t isolate t
10! - 8! =
the value of sin 178°58'
Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.
When Sara was 15 years old, an uncle left her as inheritanceà a sum of 10,000 euros which he invested in a bank that applies the interest rate of 2,5% annual. Today Sara is 18 years and wants to buy a'car, how much she can ò withdraw from the bank?
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all centers of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
simplify w+[6+(-5)]
In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.