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 Question from Shelby, a student: I can not understand how to solve this equation: Write an equation in slope-intercept form of the line that is parallel to the graph of 3y-4x=1 and passes through (0,6) please help.

Shelby,

The slope -intercept form is y = mx + b where m is the slope and b is the y-intercept. To write the equation in slope-intercept form you need the slope and the y-intercept. You find the y-intercept by locating the point on the line where it meets the y-axis, that is the point on the line with x-coordinate equal to zero. For your problem you already know that. (0,6) is on the line so 6 is the y-intercept. Thus the equation you want is y = mx + 6, and all that remains is to find the slope m.

You are told that the line is parallel to the line 3y - 4x + 1 so it has the same slope as this line. So how do you find the slope of 3y - 4x = 1? I'm going to show you using another example.

Find the slope of 4x - 5y = 2.

The technique is to rewrite the equation in its slope-intercept form, y = mx + b, and then m is the slope. For 4x - 5y = 2 I would first add -4x to each side to obtain

-5y = 2 - 4x.

next multiply both sides by -1

5y = 4x - 2,

and finally divide both sides by 5

y = 4/5 x - 2/5.

Now I have the line in slope-intercept form and I can see its slope is 4/5.

Use this technique to find the slope of 3y - 4x = 1 and substitute the slope you obtain into y = mx + 6 to obtain the equation you need.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.