Equation of line in point-slope form given 2 points

Question

Find the equation of the line in point-slope form given the two points

(2,3) and (5,-7)

Answer 1

The parent equation for point-slope form is y-y₁=m(x-x₁)

1. x₁ and y₁ represent the x and y coordinates of a coordinate pair that the line runs through
2. m represents the slope

First, you must find the slope. To find the slope you will use the equation: (y₂-y₁) / (x₂-x₁)

1. out of your two points, (2, 3) and (5, -7), you need to choose which is 1 and which is 2
2. for the purpose of this tutorial (2, 3) is 1 and (5, -7) is 2
3. (-7 - 3) / (5 - 2) which simplifies to -10/3
4. m = -10/3

Then, you can plug this into the point-slope equation as m. Next, you will need to plug in one of your points into the x₁ and y₁ variables.

1. Using (2, 3) this would look like: y-3=-10/3(x-2)

You can check this answer by plugging the other coordinate pair in for the x and y variables.

1. -7 - 3=-10/3 (5-2)
2. This can first be simplified into: -10=-10/3 (3) which can be further simplified into -10=-10
3. So long as those numbers are equivalent, you have solved to problem correctly

Hope this helps!

Answer 2

(2.3) and (5,-7) have a line through them with the equation

y-3 = ((3+7)/(2-5))(x-2)

y-3 = (-10/3)(x-2) in point slope form using the point (2.3)

or using the other point (5,-7)

y +7 = (-10/3)(x-5) is also in point slope form

-10/3 = the slope

Answer 3

Hi, thanks for your question! We can solve this in three easy steps.

1. Start off with the point-slope equation, y1-y2=m(x1-x2)
2. Clarification: m=slope of line
3. Solve the slope using the formula m=(change in y)/(change in x), or m=(y2-y1)/(x2-x1). You can use the points in either order you choose; the slope is the same either way, which I have shown below.
4. Option 1: m=(-7-3)/(5-2)=(-10/3)= -10/3
5. Option 2: m=(3--7)/(2-5)=(10/-3)= -10/3
6. Plug into y-y₁=m(x-x₁): (2,3) and (5,-7)
7. Option 1: (2,3): y-3=(-10/3)*(x-2)
8. Option 2: (5, -7): y--7=(-10/3)*(x--5)--> y+7=(-10/3)*(x-5)

Answers:

1. For (2,3): y-3=(-10/3)*(x-2)
2. For (5, -7): y+7=(-10/3)*(x-5)

Answer 4

Please remember that the co-ordinate pair ALWAYS starts with the X-axis and then the Y-Axis.

Therefore in Co-ordinate pair (2,3 ) & ( 5, -7 ), label them as

X1=2 X2 = 5

Y1=3. Y2 = -7. Use Formula rise/ run to find slope= Y2-Y1/ X2- X1= -7- ( 3 ) / 5- 2 = -10/ 3

Therefore slope = m = -10/3

Use formula for point slope equation : Y-Y1 = m ( X-X1 ) = Y-3 = -10/3 ( X- 2 )

Answer 5

Let the point-slope form be y-y1=m(x-x1) where m is the slope given by m=(y₂-y₁)/(x₂-x₁).

Note that the two points are (2, 3) and (5, -7).

Observe that x₁=2, x₂=5, y₁=3 and y₂=-7.

This gives m=(-7-3)/(5-2)=-10/3, so the slope is -10/3.

Thus y-3=-10/3(x-2).

Therefore, the equation of the line in point-slope form where the two points are (2, 3) and (5, -7) is y-3=-10/3(x-2).

Answer 6

The equation of line in point-slope from can be written as y- y1 = m(x - x1). In this case, y1 and x1 should be read as "y sub 1" and "x sub 1".

So for (2,3) and (5,-7) you need to determine the slope of the line defined by the two points first. Using the rise over the run, we get (-7 - 3) / (5 - 2) = -10/3. Since the slope has a denominator and to try to keep thing clear, I will put parentheses around the slope for the rest of the problem.

Now that we know our slope is -10/3, we can select one of the two points to write the equation of the line in point - slope form. It doesn't matter which one you choose. If we go with the first ordered pair, (2,3), we get y - 3 = (-10/3) * (x - 2). By the way, using the second pair gives us y + 7 = (-10/3)*(x - 5)

We can check our answer by substituting the second ordered pair for x and y. When we do that, we see that -7 - 3 = (-10/3) * (5 - 2). This gives us -10 = (-10/3) * (5 - 2).Simplifying, we see that -10 = (-10/3)*(3). After the 3's cancel on the right side of the equation, we are left with -10 = -10. So everything checks out.

Answer 7