Question

Write and equation in point-slope form for the line that passes through the points (-1,4) And is perpendicular to the line Y=-2x+7

Answer 1

What is point slope form?

Let's go over what point-slope form is first off. Point-slope form is $y-y_1=m(x-x_1)$, where y_1 represents the y-coordinate of the point we are given, m represents the slope of the line, and x_1 represents the x-coordinate of the point we are given.

Perpendicular line slopes; finding the slope of the line.

Since the line is perpendicular to the line y = -2x + 7, this means that the line will have an opposite reciprocal slope to the line. Perpendicular lines have opposite reciprocal slopes, meaning that they are opposites (for ex. 3 and -3) and are also reciprocals (for ex. 3 and 1/3).

The slope of the given line (y = -2x + 7) is -2, so the opposite reciprocal of this slope would be 1/2. The slope of the line we are trying to write an equation for is 1/2.

Substitute in the slope, and x and y coordinates into the point slope form equation to make an equation for the line that is perpendicular to the given line.

Substituting known values into point slope form.

$y-(4)=\frac{1}{2} [x-(-1)]$

The final step to this problem (because we are keeping it in point slope form) is to remove the parentheses around the numbers we substituted in by changing the double negative signs to a positive.

$y-4=\frac{1}{2} (x+1)$

Answer 2

since it is perpendicular line you have to change thing signs of the equation.

x    y

(-1,4)

replace the (-1) with x and (4) with y

y=1/2x+b    

4=1/2(-1)+b

4=-1/2+b

4+1/2=b

9/2=b

therefore, the perpendicular line is y=1/2x+9/2