Write the slope-intercept form of the equation of the line described.

Question

Through: (2,3), perpendicular to y=-2x-5. Please explain all steps, I have no idea where to even begin.

Answer 1

I suggest you begin by reading your textbook. There is a lot of good stuff in it.

y=mx+b is the equation of a line

through (2,3) and perpendicular to y=-2x-5

two lines are perpendicular to each other if their slopes are negative reciprocals of each other

y=-2x-5

the slope is -2

its negative reciprocal is 1/2

so we have y=(1/2)x+b so far where b is the y-intercept

the line goes through (2,3)

3=(1/2)(2)+b

3=1+b

b=2

the equation is y=(1/2)x+2

Answer 2

1. If the line is perpendicular to y=-2x-5, that means that the new line will have a slope that is the negative reciprocal of the slope -2.
2. The negative reciprocal means -(-1/2) = +1/2
3. We know that the line passes through (2,3) so we can plug it into the new equation y-y₁=m(x-x₁)
4. We know the slope +1/2
5. We know y₁=3
6. We know x₁=2
7. Point slope form: y-y₁=m(x-x₁)
8. y-3=1/2(x-2)
9. Slope intercept form: y=mx+b
10. y-3=1/2(x-2)
11. y-3=1/2x-1
12. y=1/2x-1+3
13. y=1/2x+2

Answer 3

The slope-intercept form of an equations is: Y = mx+b.

STEP 1: Find the equation of line with given values.

The line is passing through (2,3) and perpendicular to y= -2x -5

The slope of any line perpendicular to other line has a slope, (let's say m2) m2 = -1/m1

Where m1 is slope of the line y= -2x -5

Since the above line is in the form y = mx+b

m= -2 => m1= -2

then m2 = -1/m1 => m2= -1/ -2) => m2 = 1/2

We have slope and point, m2 = 1/2 and point ( 2 , 3 )

(x1,y1)

so, the point slope form of equation is: y - y1 = m (x-x1)

=> y- 3 = 1/2 (x-2)

2(y - 3) = (x-2)

2y - 6 = x - 2 ----------- 1

STEP 2 : Convert the line to slope-intercept form.

Since, we need the slope-intercept form of an equation: y = mx+b

Converting equation 1 to slope-intercept form:

2y = x - 2 + 6 {adding 3 on both the sides, to be only left with y on left hand side}

2y = x + 4

y = x /2 + 2 {dividing both the sides with 2, to be only left with y on left hand side }

Hence, the slope -intercept form of the equation is y = x /2 + 2

Hope this helps ! For any any doubts, you can message me, I am available to help you out!

Answer 4

y = -2x - 5, slope is -2

Slope of perpendicular line is 1/2 (negative reciprocal)

y = x/2 + b

To pass through (2, 3)

3 = 2/2 + b

3 = 1 + b

2 = b

y = x/2 + 2