Math CentralQuandaries & Queries


Question from victoria, a student:

what is the slope of the line with the equation y=-2x+5

Hi Victoria,

Let's find two points on this line and then calculate the slope of the line using these points. First of all let $x = 0$ and then $y = -2 \times 0 + 5 = 5$ and hence the point $(0, 5)$ is on the line. For a second point I am going to take $x = 1$ and then $y = -2 \times 1 + 5 = 3$ so $(1, 3)$ is also on the line. Find the slope of the line through $(0, 5) \mbox{ and } (1, 3).$ I got the slope to be $-2,$ did you?

So the line $y = -2 x + 5$ has slope $-2.$ Can you do this in general? Suppose $m$ and $b$ are numbers and you have the equation $y = m x + b.$ Use the same technique that I used above to see if the slope of this line is $m.$


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