Find an equation of the line containing the given pair of points
(2,1) and (6,3)
Is this the right answear?
y=(1/5x)-(3/5)
No. The slope is
m = (y2-y1)/(x2-x1) = (3-1)/(6-2) = 1/2
Take it from there.
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To find the equation of a line passing through two given points, you can use the slope-intercept form of a linear equation, which is y = mx + b.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two given points.
For the given points (2,1) and (6,3), the slope (m) can be calculated as:
m = (3 - 1) / (6 - 2) = 2 / 4 = 1/2
Now that we have the slope (m), we can substitute one of the given points into the slope-intercept form to find the y-intercept (b). Let's use the point (2,1):
1 = (1/2)(2) + b
1 = 1 + b
b = 1 - 1
b = 0
Therefore, the y-intercept (b) is 0.
Now we can write the equation of the line using the slope-intercept form:
y = (1/2)x + 0
y = (1/2)x
So, the correct equation of the line passing through the points (2,1) and (6,3) is:
y = (1/2)x