What is the equation of the line passing through (34,5) and (4,-31)?

2 Answers
Nov 11, 2015

y = (6x-179)/5.

Explanation:

We will set up the co-ordinates as:
(34, 5)
(4, -31).

Now we do subtraction of the xs and the ys.

34 - 4 = 30,
5 -(-31) = 36.

We now divide the difference in y over that in x.

36/30 = 6/5.
So m (gradient) = 6/5.

Equation of a straight line:
y = mx +c. So, let's find c. We substitute values of any of the coordinates and of m:
5 = 6/5 * 34 + c,
5 = 204/5 + c,
c = 5 - 204/5,
c = -179/5. So,

y = (6x-179)/5.

Nov 11, 2015

color(blue)(y= 6/5x-35.8)

Explanation:

Standard form equation is:

color(blue)(y=mx+c............................(1))

Where m is the slope (gradient) and c is the point where the plot crosses the y-axis in this context.

The gradient is the amount of up (or down) of y for the amount of along for the x-axis. color(blue)("Always considered from left to right .")

So m -> (y_2-y_1)/(x_2-x_1) = ((-31)-5)/(4-34)

As (34,5) is listed first you assume this is the left most point of the two.

m= (-36)/(-30) dividing negative into negative gives positive

color(blue)(m=(36)/(30) = 6/5 .........................(2))

Substitute (2) into (1) giving:

color(blue)(y=6/5x+c............................(3))

Now all we need to do is substitute known values for x and y to obtain that for c

Let (x,y) -> (34,5)

Then y=6/5x+c" " becomes:

color(brown)(5=(6/5 times 34) +c) color(white)(xxx)brackets used for grouping only

Subtract color(green)((6/5 times 34)) from both sides giving

color(brown)(5) -color(green)((6/5 times 34)) color(white)(xx) = color(white)(xx)color(brown)( ( 6/5 times 34)) -color(green)((6/5 times 34))color(brown)( +c)

c=5-(6/5times 34)

color(blue)(c = -35.8....................................(4))

Substitute (4) into (3) giving:

color(blue)(y= 6/5x-35.8)