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If there are given two points, (x1, y1) and (x2, y2), then you can write the equation of a line by finding the slope first [slope = m = (y2 - y1)/(x2 - x1)] and using one of the points in order to write the equation in the point-slope form such as
(y - y1) = m(x - x1)
y - y1 = mx - mx1
y = mx - mx1 + y1
y = mx + (y1 - mx1) the slope-intercept form, where m is the slope and (y1 - mx1) is the y-intercept.
mx - y = mx1 - y1 the general form of the equation of the line.
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Can you write the equation of a line with one point on the line?
No, you need either two points, one point and a slope, one point and a y-intercept, or a y-intercept an a slope. You can also write the equation of a line with an equation of another line but you would have to know if it is parallel or perpendicular.
Can you find an equation of the line containing the given pair of points 0 -6 and 4 2?
Suppose the equation of the line is y = mx + c where m and c need to be determined. The slope of the line = (difference in y-coordinates of the two given points)/(difference in x-coordinates of the two given points) = (-6 - 2)/(0 - 4) = -8/-4 = 2 So m = 2 ie the equation of the line becomes: y = 2x + c where c still needs to be determined. The point (0, -6) is on the line. That is, when x = 0, y = -6. Substituting in the equation, -6 = 2*0 + c so that c = -6 and the equation of the line is y = 2x - 6
What is a solution of a linear equation in two variables?
The solution of a linear equation in two variable comprises the coordinates of all points on the straight line represented by the equation.
What are the following points on the line given by the equation y 2x?
As Anand said, the question is vague. However, two important points for any equation are the x and y intercepts. For y = 2x, the x-intercept is (0,0) and the y-intercept is (0,0). Not sure if that helps.
What is the equation of the circle through -2 -4 60 and 15?
Given any two points, there are infinitely many coplanar circles that can go through the two points. And then each circle can be rotated through infinitely many planes about the straight line joining those two points. So as stated, there is not the slightest hope of pinning down an answer.
