the line containing the points x=5+2t and y=-3+t. write the slope-intercept form of the equation of the line
well. y=mx+b b is the y intercept and m is the slope. that's slope intercept form. so think about it. ill try to figure it out.
y=2x+2 i think
To write the slope-intercept form of the equation of a line, we need to find the slope and the y-intercept of the line.
The given line is specified by the equations x = 5 + 2t and y = -3 + t, where t represents a parameter.
To find the slope, we need to determine the change in y divided by the change in x. In other words, we need to find dy/dx. From the given equations, we can observe that y = -3 + t, which implies t = y + 3. Substituting this value into x = 5 + 2t, we have:
x = 5 + 2(y + 3)
x = 5 + 2y + 6
x = 2y + 11
Now, we can express y in terms of x and simplify the equation:
x = 2y + 11
2y = x - 11
y = (x - 11)/2
The equation is now in the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. In this case, the slope (m) is 1/2, and the y-intercept (b) is -11/2.
Therefore, the slope-intercept form of the equation of the line is: y = (1/2)x - 11/2.