# Math Cumulative Review: Find the equation of a Line

• MHB
• Mathlete2
In summary, to find the equation of a line perpendicular to y= -1/2x-5 and passing through (6, -4), you can use the point-slope form y-y1 = mperp(x-x1) and the information that perpendicular lines have negative reciprocals. When x=6, y=-4, so substituting these values into the equations in options (3) and (4) gives y=2x+14 and y=2x-16, respectively.
Mathlete2
Hey there! Currently struggling through a cumulative review, so I will posting a lot more questions.

An equation of a line perpendicular to the line represented by the equation y= -1/2x-5 and passing through (6, -4) is

1) y= -1/2x + 4
2) y= -1/2x - 1
3) y= 2x + 14
4) y= 2x - 16

I know it's not 1 or 2 because perpendicular lines have to be negative reciprocals. What I don't know is how to figure out whether the answer is 3 or 4.

point-slope form ...

$y-y_1 = m_{\perp}(x -x_1) \implies y-(-4) = 2(x-6)$

simplify

Mathlete said:
Hey there! Currently struggling through a cumulative review, so I will posting a lot more questions.

An equation of a line perpendicular to the line represented by the equation y= -1/2x-5 and passing through (6, -4) is

1) y= -1/2x + 4
2) y= -1/2x - 1
3) y= 2x + 14
4) y= 2x - 16

I know it's not 1 or 2 because perpendicular lines have to be negative reciprocals. What I don't know is how to figure out whether the answer is 3 or 4.

You are also told that when x= 6, y= -4. What do you get for y when you put x= 6 in either (3) or (4)?

## 1. How do I find the equation of a line using math cumulative review?

To find the equation of a line, you will need to know the slope and y-intercept. You can use the formula y = mx + b, where m is the slope and b is the y-intercept, to write the equation. The slope can be found by using the formula (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The y-intercept can be found by substituting the coordinates of one of the points into the equation y = mx + b and solving for b.

## 2. What is the difference between finding the equation of a line using points and using slope and y-intercept?

When finding the equation of a line using points, you are given two points on the line and use the slope formula to find the slope. Then, you can plug the slope and one of the points into the point-slope form of the equation, y - y1 = m(x - x1), to write the equation. When using slope and y-intercept, you are given the slope and y-intercept and use the formula y = mx + b to write the equation.

## 3. Can I use any two points on the line to find the equation?

Yes, you can use any two points on the line to find the equation. However, it is recommended to use points with whole number coordinates to make the calculations easier.

## 4. What if I am given the slope and a point on the line, but not the y-intercept?

If you are given the slope and a point on the line, you can use the point-slope form of the equation, y - y1 = m(x - x1), to write the equation. Simply plug in the given slope and point into the formula to find the equation.

## 5. Can I use the equation of a line to find the slope and y-intercept?

Yes, you can use the equation of a line, y = mx + b, to find the slope and y-intercept. The slope is represented by the coefficient of x (m) and the y-intercept is represented by the constant term (b).

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