Luna200idn
Answered

Find the best solutions to your problems with the help of IDNLearn.com's experts. Get accurate and comprehensive answers from our network of experienced professionals.

. If (5, 7) and (-3, 0) lie on the line ax - by = -20.

i) Find the value of a & b. [IM]
ii) Write the equation of the line in standard form.
iii) Find the coordinate of the point of intersections of the given line with x-axis and y-axis respectively.
iv) Find two more solutions of the given line. ​

Sagot :

Xero099idn

i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).

iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.

How to derive the equation of a line?

In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:

5 · a - 7 · b = - 20

- 3 · a = - 20

Whose solution is a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) Now we find the coordinates of the intercepts of the line:

x-Intercept

(20 / 3) · x = - 20

x = - 3

y-Intercept

(160 / 21) · y = - 20

y = - 21 / 8

iv) We can find two alternative solutions by using multiples:

20 · x + (160 / 7) · y = - 60

140 · x + 160 = 420

To learn more on equations of the line: https://brainly.com/question/21511618

#SPJ1

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.