The equation of the line passing through (1,8) and (5,6) can be expressed in the form (x/a)+(y/b)=1. Find a.
Please help, I don't know how to put my slope intercept equation into that form. I found the slope intercept form to be y= -(1/2)x+17/2. Thanks!
good so far at y= -(1/2)x+17/2
multiply each term by 2
2y = -x + 17
x + 2y = 17
now, instead of the 17 you want 1, so divide each term by 17
x/17 + 2y/17 = 1
x/17 + y/(17/2) = 1 compare with x/a + y/b = 1
so a = 17, b = 17/2
btw, have you learned that if written in that form
a is the x-intercept and
b is the y-intercept, neat eh??
Ohh, thanks! I was actually sick the day of the class, and my teacher wasn't there in our most recent class so I just did the problems to the best of my ability, so I didn't know about that a/b form. Thanks again! :)
To find the value of 'a' in the equation (x/a) + (y/b) = 1 for the line passing through (1,8) and (5,6), we can first rewrite the given equation in slope-intercept form (y = mx + b) and then compare it with the general equation to determine the value of 'a'.
From the given information, you have derived the slope-intercept form as y = -(1/2)x + 17/2.
To convert this equation into the standard form (Ax + By = C), we multiply the entire equation by 2 (to eliminate fractions):
2y = -x + 17.
Now re-arrange the equation to get it in the general form:
x + 2y - 34 = 0.
Comparing the above equation with the general form (Ax + By = C), we can see that 'a' corresponds to the coefficient of 'x', which is 1 in this case.
Therefore, 'a' equals 1.
So, the equation of the line passing through (1,8) and (5,6) in the form (x/a) + (y/b) = 1 is (x/1) + (y/b) = 1.