Question
A line with a slope=1/2 passes through the points (2,5) and (x,3) whate is the value of x
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GPT 3.5
We can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
Since the line has a slope of 1/2, we have the equation y = (1/2)x + b.
To find the value of b, we can use the fact that the line passes through the point (2,5). Plugging in the x and y values of this point into the equation, we get 5 = (1/2)(2) + b.
Simplifying this equation, we have 5 = 1 + b.
Subtracting 1 from both sides of the equation, we get b = 4.
So the equation of the line becomes y = (1/2)x + 4.
To find the value of x when the line passes through the point (x,3), we can plug in the y value of this point into the equation and solve for x.
Plugging in the y value of 3, we have 3 = (1/2)x + 4.
Subtracting 4 from both sides of the equation, we get -1 = (1/2)x.
Dividing both sides of the equation by 1/2, we get -2 = x.
Therefore, the value of x is -2.
Since the line has a slope of 1/2, we have the equation y = (1/2)x + b.
To find the value of b, we can use the fact that the line passes through the point (2,5). Plugging in the x and y values of this point into the equation, we get 5 = (1/2)(2) + b.
Simplifying this equation, we have 5 = 1 + b.
Subtracting 1 from both sides of the equation, we get b = 4.
So the equation of the line becomes y = (1/2)x + 4.
To find the value of x when the line passes through the point (x,3), we can plug in the y value of this point into the equation and solve for x.
Plugging in the y value of 3, we have 3 = (1/2)x + 4.
Subtracting 4 from both sides of the equation, we get -1 = (1/2)x.
Dividing both sides of the equation by 1/2, we get -2 = x.
Therefore, the value of x is -2.
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