Finding Formulas for Linear Functions

I am working on this problem that requires us to find the formula for the linear function provided.

It states: Find the equation of the line passing through the point (2,1) and perpendicular to the line y=5x-3.

I know that a perpendicular line is going to have the opposite slope, so I figured I would plug in the points given to a perpendicular equation.

y=(-1/5)(2)-1
y=(-2/5)-1
y=(-7/5)

Would I then use y=(-7/5) as the y-intercept and get: y(x)=(-1/5)x-(7/5)

Or should I plug zero in for the x value:
y=(-1/5)(0)-1
y=-1

Giving me -1 as the y-intercept and the equation: y(x)=(-1/5)x-1



Thank you in advance.

NK8485 said:

I am working on this problem that requires us to find the formula for the linear function provided.

It states: Find the equation of the line passing through the point (2,1) and perpendicular to the line y=5x-3.

I know that a perpendicular line is going to have the opposite slope, so I figured I would plug in the points given to a perpendicular equation.

y=(-1/5)(2)-1
y=(-2/5)-1
y=(-7/5)

Would I then use y=(-7/5) as the y-intercept and get: y(x)=(-1/5)x-(7/5)

Or should I plug zero in for the x value:
y=(-1/5)(0)-1
y=-1

Giving me -1 as the y-intercept and the equation: y(x)=(-1/5)x-1



Thank you in advance.

Click to expand...

Well, you are SORT OF on the right track.

The equation of the given line is
y = 5x - 3
This is "slope-intercept form", y = mx + b, so the slope of this line is 5.

The slopes of perpendicular lines are opposite reciprocals, not just opposites. If the given line has a slope of 5, then any line perpendicular to this line will have a slope of -1/5. You USED this slope, apparently, but you tried to combine too much into one step, and as a consequence, you did not get the correct solution.

Now we know that the line we are looking for, the perpendicular, has a slope of -1/5, so we can begin to write its equation:
y = mx + b
y = (-1/5)x + b

And we want this line to contain the point (2, 1). So, the point (2, 1) must satisfy the equation
y = (-1/5)x + b
Substitute 2 for x and 1 for y in THIS equation (I think you substituted into something else, but I'm not at all sure WHAT!!).

1 = (-1/5)*2 + b
1 = (-2/5) + b
1 + (2/5) = (-2/5) + b + (2/5)
7/5 = b

Ok...the y-intercept of this desired perpendicular line is 7/5, and we can write the equation:

y = (-1/5)x + (7/5)

Your work was "close but no cigar." Please slow down....don't try to combine or skip steps; doing so often leads to careless mistakes.

Since you got two different equations as possible answers, you should have recognized that you had done something(s) incorrectly. That's a BIG hint to start over, and work very carefully.

Thank you for the help.

Yeah, I think I got mixed up on where to plug in the x and y values given.

Instead of plugging the y value (1) in for f(x) I plugged it in for the y-intercept value b which gave me an incorrect answer.