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Theresa L.

asked • 03/31/14

linear equation help

Consider the linear equation 2x – 5y = 3.
(a) Write the linear equation in slope-intercept form.
(b) State the value of the slope.
(c) State the y-intercept for this line.
(d) State a point on this line other than the y-intercept.

1 Expert Answer


Theresa L.

I am still having trouble 


Stephen W.

a) 2x – 5y = 3
Subtract 2x from both sides:
    2x - 5y - 2x = 3 - 2x
Now you have:
-5y = 3 - 2x
Divide both sides by -5:
y = (3 - 2x)/-5
You now have to divide both terms by -5, individually:
y = (3/-5) - (2x/-5)
(2x/-5) should be rewritten as (-2/5)x
y = (-3/5) - (-2/5)x
"add the opposite":
y = (-3/5) + (+2/5)x
Now we need to put it all into y=(m)x+(b) form:
y = (2/5)x - (3/5)
Slope is m (2/5), y-intercept is b (-3/5)
OK. Now that you have the equation for this line, we have the x and y variables. These are simply coordinate points on a graph. If you plug a number in for x, then do the math and solve for y, you will have the coordinates for a point on this line. The y-intercept has an x coordinate of zero - (0,y). This means that you plug in a zero where the x is, and solve for y. In our problem, if x is zero, then x times (2/5) is zero. All that is left is y = -3/5. So the coordinates are (0,-3/5). This is a point on this line. Now you can plug in another number for your x, and solve for the y. This will be another set of coordinates on this line. Hint: Most of the time people like to use 1 or -1 for x.
Let me know if you need any more help!


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