Question

What is the equation of this line (4,5),(-2,-3)

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

To find the slope we need two points. According to the data we have:
`(x1, y1) :( 4,5)\\(x2, y2): (- 2, -3)`

So:

`m = \frac {y2-y1} {x2-x1} = \frac {-3-5} {- 2-4} = \frac {-8} {- 6} = \frac {4} {3}`

Thus, the equation is of the form:

`y = \frac {4} {3} x + b`

We make a point and find b:

`5 = \frac {4} {3} (4) + b\\5 = \frac {16} {3} + b\\b = 5- \frac {16} {3}\\b = \frac {15-16} {3}\\b = -\frac {1} {3}`

Finally we have:

`y = \frac {4} {3} x - \frac {1} {3}`

Answer:

`y = \frac {4} {3} x - \frac {1} {3}`

Answer 2

y = 4x/3 - 1/3.

Explanation:

The equation of the straight line is given by the following formula:

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1); where (x, y) is the general point, (x1, y1) is the first point on the line, and (x2, y2) is the second point on the line.

Given that (x1, y1) = (4, 5) and (x2, y2) = (-2, -3):

(y - 5)/(x - 4) = (-3 - 5)/(-2 - 4).

(y - 5)/(x - 4) = -8/-6.

(y - 5)/(x - 4) = 4/3.

Cross multiplying:

3*(y - 5) = 4*(x - 4).

3y - 15 = 4x - 16.

3y = 4x - 1.

y = 4x/3 - 1/3.

This the equation of the line in the y = mx + c form!!!