Find the value of a such that the points (3, a) and (5, 3a) lie on a line with slope m= 1/3.

Question

Any help would be granted. Thank You.

Answer 1

the line has a general form y = mx + c, where m is the slope and c is the intercept.

Here your coordinates of two given points should match with the line which has y = (1/3)x+c

Now let's substitute our first coordinate to the line equation.

(3,a)

a = (1/3)*3 + c (1)

substitute our second coordinate to the line equation.

(5, 3a)

3a = (1/3)*5 + c (2)

now we are looking for "a" value

solving (2) and (1) by subtracting (1) from (2)

(2) - (1)

2a = (1/3)*2

== a = (1/3)

you can find the intercept as well

(1)*3 - (2)

c = - 2/3