The slope of the line joining the points (-1,5) and (6,-2) is -1
x + y = 4 is the equation of line
x intercept is (-4, 0)
y intercept is (0, 4)
<em><u>Solution:</u></em>
Given that,
Points are (-1,5) and (6,-2)
<em><u>The slope of line is given as:</u></em>
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
From given,
![(x_1, y_1) = (-1, 5)\\\\(x_2, y_2) = (6, -2)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%28-1%2C%205%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%286%2C%20-2%29)
Substituting the values we get,
![m = \frac{-2-5}{6+1}\\\\m = \frac{-7}{7}\\\\m = -1](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2-5%7D%7B6%2B1%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-7%7D%7B7%7D%5C%5C%5C%5Cm%20%3D%20-1)
Thus slope of line is -1
<em><u>The equation of line in slope intercept form is given as:</u></em>
y = mx + c -------- eqn 1
Where,
m is the slope
c is the y intercept
Substitute m = -1 and (x, y) = (-1, 5) in eqn 1
5 = -1(-1) + c
5 = 1 + c
c = 4
Substitute m = -1 and c = 4 in eqn 1
y = -x + 4
In standard form,
x + y = 4 is the equation of line
<em><u>Find x intercept:</u></em>
Substitute y = 0
x + 0 = 4
x = -4
Thus x intercept is (-4, 0)
<em><u>Find y intercept:</u></em>
Substitute x = 0
0 + y = 4
y = 4
Thus y intercept is (0, 4)