We need to find the slope of the given equation by converting it to the slope intercept form:  $\displaystyle y=-\frac{2}{5}x+\frac{9}{5}$. 

The slope is $\displaystyle -\frac{2}{5}$ and the perpendicular slope would be the opposite reciprocal, or $\displaystyle \frac{5}{2}$. 

The new equation is of the form $\displaystyle y=\frac{5}{2}x+b$ and we can use the point $\displaystyle (4,12)$ to calculate $\displaystyle b=2$. The next step is to convert $\displaystyle y=\frac{5}{2}x+2$ into the standard form of $\displaystyle -5x+2y=4$.

Perpendicular slopes are opposite reciprocals.  The original slope is $\displaystyle -\frac{1}{3}$ so the new perdendicular slope is 3.

We plug the point $\displaystyle (1,7)$ and the slope $\displaystyle m=3$ into the point-slope form of the equation:

$\displaystyle y-y_{1}=m(x-x_{1})$

to get $\displaystyle y=3x+4$ or in standard form $\displaystyle -3x+y=4$.

First one needs to use one of the two equations to substitute one of the unknowns.

From the second equation we can derive that y = x – 3.

Then we substitute what we got into the first equation which gives us: x + x – 3 = 15.

Next we solve for x, so 2x = 18 and x = 9.

x – y = 3, so y = 6.

These two lines will intersect at the point (9,6).

We are given an equation of a line and told that line A is perpendicular to it.  The slope of the given line is 2.  Therefore, the slope of line A must be $\displaystyle -0.5$, since perpendicular lines have slopes that are negative reciprocals of each other.

The equation for line A will therefore take the form $\displaystyle y=-0.5x+b$, where b is the y-intercept.

Since we are told that it crosses $\displaystyle (0,1)$, we can plug in the point and solve for c:

$\displaystyle 1 = -0.5(0)+b$

$\displaystyle b=1$

Then the equation becomes $\displaystyle y=-0.5x+1$.

To find the x-intercept, plug in 0 for y and solve for x:

$\displaystyle 0=-0.5x+1$

$\displaystyle 0.5x=1$

$\displaystyle x=2$

The slope of the given line is $\displaystyle m = -2$, and the slope of the perpendicular line is its negative reciprocal, $\displaystyle m = 1/2$.  We take the new slope and the given point $\displaystyle (2,4)$ and plug them into the slope-intercept form of a line, $\displaystyle y = mx + b$.

$\displaystyle 4 = \frac{1}{2}\times 2+b$

 $\displaystyle b = 3$

Thus, the perpendicular line has the equation $\displaystyle y = \frac{1}{2}x + 3$, or in standard form, $\displaystyle -x + 2y = 6$.

We start by add x to the other side of the equation to get the y by itself, giving us 8y =17 + x. We then divide both sides by 8, giving us y= 17/8 + 1/8x. Since we are looking for the equation of a perpendicular line, we know the slope (the coefficient in front of x) will be the opposite reciprocal of the slope of our line, giving us y= -8x + 5 as the answer.

Convert the equation to slope intercept form to get y = –1/3x + 2.  The old slope is –1/3 and the new slope is 3.  Perpendicular slopes must be opposite reciprocals of each other:  m_{1 *} m₂ = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

Convert the given equation to slope-intercept form.

$\displaystyle 3x + 5y = 15$

$\displaystyle 5y=-3x+15$

$\displaystyle y=-\frac{3}{5}+3$

The slope of this line is $\displaystyle -\frac{3}{5}$. The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is $\displaystyle \frac{5}{3}$.

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

$\displaystyle 2 = \frac{5}{3}(3) + b$

$\displaystyle 2=5+b$

$\displaystyle b = -3$

So the equation of the perpendicular line is $\displaystyle y = \frac{5}{3}x - 3$.

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

The slope of m is equal to   ^y2-y1/_x2-x1  =  ^2-4/_5-1 = ^-1/₂                                  

Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be –1:

(slope of p) * (^-1/₂) = -1

Slope of p = 2

So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.