Find the slope and write the equation of the given line.

The correct answer is: Slope of the given line is 1 and equation of the given line is x - y = -2.

Step-by-step solution:-
From the given diagram, we can observe that the given line passes through 2 points i.e. A(-2,0) and B(0,2)
Hence, x1 = -2, y1 = 0; x2 = 0 & y2 = 2
From the given information, we can observe that the given line passes through points A and B.
Using the 2point formula for slope of a line, we get-
Slope = m = y2 - y1 / x2 - x1
= 2 - 0 / 0 - (-2)
= 2 / 0 + 2
= 2 / 2
Slope = m = 1 ............................................ (Equation i)
We can find the equation of the given line using one of the points that it passes through and its slope.
We take Point (-2,0) i.e. x1 = -2 and y1 = 0 and m = 1 from equation i and write the equation in slope point form as-
y-y1 = m (x-x1)
∴ y - 0 = 1 [x - (-2)]
∴ y - 0 = 1 (x + 2)
∴ y = x + 2
∴ y - x = 2
i.e. x - y = -2 ................................... (Multiplying both sides by -1)
Final Answer:-
∴ Slope of the given line is 1 and equation of the given line is x - y = -2.
Note:-
Alternatively, 2 point form can also be used to find the equation as the given line passes through (-2,0) & (0,2).
X1 = -2, y1 = 0; x2 = 0 & y2 = 2
y - y1 = (y2-y1) (x - x1)
(x2-x1)
y - 0 = (2 - 0) [x - (-2)]
[0 - (-2)]
∴ y = 2 × (x + 2)
0 + 2
∴ y = 2 × (x + 2)
2
∴ y = 1 × (x + 2)
∴ y = x + 2
∴ -2 = x - y
i.e. x - y = -2
Hence, Answer remains the same.