find equation of linear function g perp. to 5x-3y=6

[santaclaus]

Find the equation of the linear function g whose graph is perpendicular to the line 5x-3y=6; the two lines intersect at x=15 (Do you have any rules for me to follow ? I can't remember how to do this) thanks

[stapel_eliz]

Find the equation of the linear function g whose graph is perpendicular to the line 5x-3y=6; the two lines intersect at x=15 (Do you have any rules for me to follow ? I can't remember how to do this) thanks

What is the y-value at the intersection point? Since the point in question is where both lines cross, then whatever the y-value for "g" is, it's the same as the y-value for the given line. So plug the given x-value into the given line equation, and find the necessary y-coordinate.

Solve the given equation for "y=", and read the slope value off the slope-intercept form of the line. Then use this to find the perpendicular slope's value.

Now that you have a point and a slope, plug them into the point-slope form. Solve again for "y=", but rename "y" as "g" to get the function they're looking for.

[santaclaus]

[color=#FF0000]so if I solve for y, I get -3y=6-5x
then, y=5/3x +2
so, do I then do y-y₁= -3/5(x-15) +2? and

[stapel_eliz]

so if I solve for y, I get -3y=6-5x
then, y=5/3x +2

Check your signs:

steps:
 5x - 3y = 6
-5x           -5x
-----------------
     -3y = 6 - 5x
     ---   ------
      -3     -3

           6    -5x
      y = --- + ---
          -3    -3

Simplify to get the line equation. Read off the value of the slope. (You've got that right, but you'll want to correct the intercept before you hand in your work.) Then use what you learned when you studied the lesson on slope (in the link provided earlier) to find the perpendicular slope.

[santaclaus]

so perpendicular to this would be y=-3/5x-2 because I took the reciprocal and opposite sign for slope. Now what does it mean when the two lines intersect at x=15? where would i insert x=15? in this equation y=-3/5-2? or the initial one ?

[stapel_eliz]

so perpendicular to this would be y=-3/5x-2 because I took the reciprocal and opposite sign for slope.

Yes. As shown in the previous reply, the slope of the given line is m = 5/3, so the slope of the perpendicular line would have to be m_perp = -3/5.

Now what does it mean when the two lines intersect at x=15?

As mentioned earlier, when lines intersect, they share a point. So plug the given x-value into the given line equation, and simplify to find the y-value for the intersection point.

where would i insert x=15? in this equation y=-3/5-2? or the initial one ?

Um... Aren't they the equations for the same line...? Didn't we only just re-arrange it?