Find the equation of a line in slope-intercept form whose parametric equations are x=2t+3 and y=4t-1.
x=2t+3
t= x/2 -3
y=4t-1
t= y/4+1
x/2-3=y/4+1
rearrange that into standare slope form.
To find the equation of the line in slope-intercept form, we need to express y in terms of x.
First, let's eliminate the parameter t from the given parametric equations. We can do this by solving both equations for t:
x = 2t + 3 (1)
y = 4t - 1 (2)
Rearranging equation (1) gives us:
t = (x - 3) / 2
Substituting this expression for t in equation (2) gives us:
y = 4((x - 3) / 2) - 1
Simplifying this equation gives us:
y = 2x - 7
Now we have the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 2 and the y-intercept is -7.
Therefore, the equation of the line in slope-intercept form is y = 2x - 7.