Question

Find the equation in slope-intercept form that describes each line through (2, –3) and (7, 9)

Answer 1

y = 12x/5 - 39/5.

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) = (2, -3) and (x2, y2) = (7, 9):

(y - (-3))/(x - 2) = (9 - (-3))/(7-2).

(y + 3)/(x - 2) = 12/5.

Cross multiplying:

5*(y + 3) = 12*(x - 2).

5y + 15 = 12x - 24.

5y = 12x - 39.

y = 12x/5 - 39/5.

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

Answer 2

For this case we have that by definition, an equation of the line of 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

We have two points through which the line passes, then we find the slope:

`(x1, y1) :( 2, -3)\\(x2, y2) :( 7,9)\\m = \frac {y2-y1} {x2-x1} = \frac {9 - (- 3)} {7-2} = \frac {9 + 3} {5} = \frac {12} {5}`

Then, the equation is of the form:

`y = \frac {12} {5} x + b`

We substitute a point and find b:

`-3 = \frac {12} {5} (2) + b\\-3 = \frac {24} {5} + b\\b = -3- \frac {24} {5}\\b = - \frac {39} {5}`

Finally we have:

`y = \frac {12} {5} x- \frac {39} {5}`

Answer:

`y = \frac {12} {5} x- \frac {39} {5}`