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Mathematics

Grade-8

Easy

Question

What are the slope and y-intercept of this line?

Slope: –2, y-intercept: –1
Slope: –2, y-intercept: 1
Slope: 2, y-intercept: –1
Slope: 2, y-intercept: 1

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. Y-intercept of a line is the value of y-coordinate when x = 0.

The correct answer is: Slope: 2, y-intercept: –1

GIVEN-
Points (2,3) and (0,-1) are on the given line.
TO FIND-
Slope and y-intercept
SOLUTION-
From the given graph, we can observe that the given line passes through the points (2,3) and (0,-1).

Hence, x1 = 2, y1 = 3, x2 = 0 and y2 = -1.
∴ Slope = m = y2-y1 / x2-x1
∴ Slope = m = (-1 - 3) / (0 - 2)
∴ Slope = m = -4/-2
∴ Slope = m = 2
We know that y-intercept is the point where x = 0.
From the given graph, we observe that for x = 0, the corresponding value of the y-coordinate is -1.
FINAL ANSWER-
Option 'c' i.e. 'Slope: 2, y-intercept: –1' is the correct answer to the given question.

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