Answer:
y = 12x/5 - 39/5.
Step-by-step 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!!!
For this case we have that by definition, an equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
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:
[tex](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}[/tex]
Then, the equation is of the form:
[tex]y = \frac {12} {5} x + b[/tex]
We substitute a point and find b:
[tex]-3 = \frac {12} {5} (2) + b\\-3 = \frac {24} {5} + b\\b = -3- \frac {24} {5}\\b = - \frac {39} {5}[/tex]
Finally we have:
[tex]y = \frac {12} {5} x- \frac {39} {5}[/tex]
Answer:
[tex]y = \frac {12} {5} x- \frac {39} {5}[/tex]
