A few days ago
Anonymous

Writing the equation of a line using fractions?

I am struggling to grasp the concept of this, how can I find the slope intercept form equation (y=mx+b) then all I am given is the following info:

Write the equation of the line passing through (4/7,-2/3) and (1/3,4)?

Also using the equation 3/7x+1/4y-6=0, how can I graph using a table? (I plugged 1 in onto the x side of the table, but on they y side of the table I got 22 2/7, which I don’t think is right)

I am just having problems grasping this concept, can anyone help me please?

Top 1 Answers
A few days ago
Anand S

Favorite Answer

Use your two given points to find the slope of the line that passes between them.

Slope of a line = (change in y)/(change in x). So for the change in y, subtract the y-coordinate of one point from the y-coordinate of the other point. For the change in x, do the same thing with the x-coordinates. It doesn’t matter which point you start with, but you *have* to start with the *same* point both times (calculating change in y and then calculating change in x).

Once you have the slope of your line (hint: it will be a negative fraction that you can reduce to a denominator of 5), remember that y = mx + b gives you a formula for finding all the points that fall on a particular line. So that means either one of your points will “solve” the equation y = mx + b, since they are both on the line. Pick *one* of your two points and plug it into the y = mx + b equation. You know x and y (they are the coordinates of whichever point you chose), and you know the slope m because you just calculated it. You can solve for your one unknown, the y-intercept b.

Once you have m and b, you know the slope-intercept form of the equation. To check that you did it right, do the whole thing again, using the *other* point first when doing the slope calculations, and then finding b using the point you didn’t use the first time. Both methods will give you the same answer.

As for graphing using a table, your answer of (1, 22 2/7) is right. Plug in values for x and calculate the output values of y. Then take those pairs of numbers (the x you put in and the y you got out) and plot them as points on a grid. Connect the points in a line to finish your task of graphing with a table.

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