We need to find the slope of the given equation by converting it to the slope intercept form:.

The slope is和垂直坡会相反reciprocal, or.

The new equation is of the formand we can use the pointto calculate. The next step is to convertinto the standard form of.

Perpendicular slopes are opposite reciprocals. The original slope isso the new perdendicular slope is 3.

We plug the pointand the slopeinto the point-slope form of the equation:

to getor in standard form.

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

从第二个方程我们可以推出y=x– 3.

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

接下来,我们解出x, so 2x= 18 andx= 9.

x–y= 3, soy= 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, since perpendicular lines have slopes that are negative reciprocals of each other.

The equation for line A will therefore take the form, where b is the y-intercept.

年代ince we are told that it crosses, we can plug in the point and solve for c:

Then the equation becomes.

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

The slope of the given line is, and the slope of the perpendicular line is its negative reciprocal,. We take the new slope and the given pointand plug them into the slope-intercept form of a line,.

Thus, the perpendicular line has the equation, or in standard form,.

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 gety= –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+bor 5 = 3(1) +b, sob= 2

年代oy= 3x+ 2

Convert the given equation to slope-intercept form.

The slope of this line is. The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is.

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

年代o the equation of the perpendicular line is.

First, put the equation of the line given into slope-intercept form by solving fory. You gety= -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 equationy= 1/2x+band solving forb, we getb= 6. Thus, the equation of the line isy= ½x+ 6. Rearranged, it is –x/2 +y= 6.

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

年代ince linepis perpendicular to linem, this means that the products of the slopes ofpandmmust be–1:

(slope ofp) * (^-1/₂) = -1

年代lope ofp= 2

年代o 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 linep. The answer is 2x – y = 3.