In the 𝑥𝑦-plane, line 𝑙 with slope 3 passes through the points 𝐴 and 𝐵. If the coordinates of point 𝐴 are (2,10), which of the following can be the coordinates of point 𝐵?
Question
In the 𝑥𝑦-plane, line 𝑙 with slope 3 passes through the points 𝐴 and 𝐵. If the coordinates of point 𝐴 are (2,10), which of the following can be the coordinates of point 𝐵?
Solution
The equation of a line in the xy-plane can be given by the formula y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that the line l has a slope of 3 and passes through the point A(2,10), we can substitute these values into the equation to find the y-intercept.
So, 10 = 3*2 + c => 10 = 6 + c => c = 10 - 6 => c = 4
So, the equation of the line l is y = 3x + 4.
Now, any point (x,y) that satisfies this equation can be a possible coordinate for point B.
For example, if we choose x = 3, then y = 3*3 + 4 = 13. So, B could be (3,13).
Similarly, if we choose x = 4, then y = 3*4 + 4 = 16. So, B could be (4,16).
And so on.
So, the coordinates of point B can be any point (x,y) that satisfies the equation y = 3x + 4.
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