Respuesta :
7x + 4y = 17 is the equation of line passing through points (3, -1) and (-1, 6)
Solution:
Given that we have to find the equation of line passing through points (3, -1) and (-1, 6)
Let us first find the slope of line
The slope of line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here in this sum,
[tex](x_1, y_1) = (3, -1)\\\\(x_2, y_2) = (-1, 6)[/tex]
Substituting the values in given formula we get,
[tex]m = \frac{6-(-1)}{-1-3}\\\\m = \frac{6+1}{-4}\\\\m = \frac{-7}{4}[/tex]
The equation of line in slope intercept form is:
y = mx + c ---------- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Find the y - intercept:
Substitute (x, y) = (3, -1) and [tex]m = \frac{-7}{4}[/tex] in eqn 1
[tex]-1 = \frac{-7}{4}(3) + c\\\\-1 = \frac{-21}{4} + c\\\\-1 = \frac{-21+4c}{4}\\\\-4 = -21+4c\\\\4c = 17\\\\c = \frac{17}{4}[/tex]
Substitute [tex]m = \frac{-7}{4} \text{ and } c = \frac{17}{4}[/tex] in slope intercept form
[tex]y = \frac{-7}{4}x + \frac{17}{4}[/tex]
Thus the equation of line in slope intercept form is found
Writing in standard form,
4y = -7x + 17
7x + 4y = 17
Thus the equation of line in standard form is also found
