SOLUTION: Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7???

Question 145656: Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7???
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Solve for y.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point .

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 4 to both sides.

Combine like terms.

So the equation of the line perpendicular to that goes through the point is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the perpendicular line (green) through the point .

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
2x+y=7
y=-2x+7 slop-intercept form
the slope (m) is -2.
The slope of a line perpendicular to this line is the negative reciprocal of its slope: 1/2 or .5
y-y[1]=m(x-x[1]) point-slope form
y-4=.5(x-4)
y-4=.5x-2
y=.5x+2 Answer
.
Below is a graph of the 2 equations. The green line is y=.5x-2. Note that it goes through the point (4,4)
.
Ed
.

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