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Mathematics

Grade-8

Easy

Question

1) Points M(2, 9) and N(–1, 3) are on a line with y-intercept –4. What is the equation of the line?

y = –4x – 2
y = –2x + 4
y = 2x – 4
y = 4x + 2

hint Hint:

1. 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.
2. Equation of a line, when its slope and intercept is given can be given as- y = mx + b, where m = slope and b = y-intercept.

The correct answer is: y = 2x – 4

GIVEN-
Points on the line- M(2, 9) and N(–1, 3)
y-intercept = b = -4
TO FIND-
Equation of the given line.
SOLUTION-
We are given that M(2, 9) and N(–1, 3) are on the given line.
Hence, x1 = 2, y1 = 9, x2 = -1 and y2 = 3
Slope = m = y2-y1 / x2-x1
∴ Slope = m = (3 - 9) / (-1 - 2)
∴ Slope = m = -6 / -3
∴ Slope = m = 2 ................................. (Equation i)
Substituting values in y = mx + b, we get-
y = 2x + (-4) ....................................... (From given information & Equation i)
∴ y = 2x - 4
FINAL ANSWER-
Option 'c' i.e. 'y = 2x – 4' is the correct answer to the given question.

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