Maths-
General
Easy
Question
Find the slope and write the equation of the given line.
Hint:
The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates.
Slope = m = rise / run = y2-y1 / x2-x1
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.
Related Questions to study
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Find the value of p so that
![left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent](data:image/png;base64,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)
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