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27 Jul 2018, 03:10
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C
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If line k is in the xy–coordinate plane, what is the slope of k?
(1) The x–intercept of k is 3.
(2) The y–intercept of k is -2.
(1) The x–intercept of k is 3.
(2) The y–intercept of k is -2.
27 Jul 2018, 03:18
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To find the slope of line k
Statement 1
The x–intercept of k is 3
=> the line k passes through the point (3,0) since y-coordinate is 0 where the line intersects x axis
There are infinite possible lines that can pass through a single point. Some of them have positive slope and some negative slope
Statement 1 is not sufficient
Statement 2
The y–intercept of k is -2
=> the line k passes through the point (0,-2) since x-coordinate is 0 where the line intersects y axis
There are infinite possible lines that can pass through a single point. Some of them have positive slope and some negative slope
Statement 2 is not sufficient
Combining statements 1 and 2
The line k passes through the points (3,0) and (0,-2)
Slope of line k is \(\frac{0-(-2)}{3-0} = \frac{2}{3}\)
Statements 1 and 2 together are sufficient
Hence option C
Statement 1
The x–intercept of k is 3
=> the line k passes through the point (3,0) since y-coordinate is 0 where the line intersects x axis
There are infinite possible lines that can pass through a single point. Some of them have positive slope and some negative slope
Statement 1 is not sufficient
Statement 2
The y–intercept of k is -2
=> the line k passes through the point (0,-2) since x-coordinate is 0 where the line intersects y axis
There are infinite possible lines that can pass through a single point. Some of them have positive slope and some negative slope
Statement 2 is not sufficient
Combining statements 1 and 2
The line k passes through the points (3,0) and (0,-2)
Slope of line k is \(\frac{0-(-2)}{3-0} = \frac{2}{3}\)
Statements 1 and 2 together are sufficient
Hence option C
27 Jul 2018, 09:37
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You need two points to define a line so yeah you need both statements.
