SOLUTION: my question is I need to write the equation for the line satisfying the given information, then write it in slope-intercept form. Graph the equation, and show both of the intercept

Algebra ->  Linear-equations -> SOLUTION: my question is I need to write the equation for the line satisfying the given information, then write it in slope-intercept form. Graph the equation, and show both of the intercept      Log On


   

Question 41518: my question is I need to write the equation for the line satisfying the given information, then write it in slope-intercept form. Graph the equation, and show both of the intercepts.
Passes through the points (10,42.3)(20,51.5)
Passes through through the points(100,2.2)(150,1.9)
passes through the poins(1/2,-1/2) with slope 1/2
passes through the points(-10.4,0.3)(5,34,000)
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
For determination of the equation of a straight line passing through two points, whose coordinates are given, see my answer to this question.

http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=41158

For the slope-intercept form of the straight line obtained as above procede as follows. If the equation be ax + by + c = 0 (in general form), then take the whole part of the equation excepting the y-part on the right. Thus you have by = -ax - c. Now divide both sides by the coefficient of y. Thus we get y+=+-%28a%2Fb%29%2Ax+-+c%2Fb. This is the slope intercept form of the st. line ax + by + c = 0 and its slope is -a%2Fb and point of intersection with y-axis is (0,-c%2Fa). To see an example refer to my solution to this question.

http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=40798

For expressing the equation of a straight line thus obtained in intercept form to find out the intercepts on the coordinate axes see my solution to this question.

http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=41324

Now, to find the equation of a st. line passing through a given point and having a given slope, follow the procedure below.
Here, we are reqd. to find a st. line whose slope is 1%2F2 and which passes through the point (1%2F2,-1%2F2).
Let the equation be y = mx + k where m = slope and k = intercept on y-axis.
So m = 1%2F2.
Hence y = 1%2F2x + k
or 2y = x + 2k
Now, this st. line passes through the point (1%2F2,-1%2F2) so its equation must be satisfied by the coordinates of this point.
Hence, 2%2A%28-1%2F2%29+=+1%2F2+%2B+2k
or 2k+=+-1%2F2+-+1+=+-3%2F2
or k+=+%28-3%2F2%29%2F2+=+-3%2F4
Thus the reqd. equation of the given st. line is
2y+=+x+%2B+2%28-3%2F4%29
or 2y+=+x+-+3%2F2
or 2x - 4y = 3
Now, express this equation in intercept form and get the answer.

Draw the graphs yourself.