algebra 2 or algebra 1

Question

Write an equation in standard form for the line that passes through the given points.

(2, 7) and (−5, 2)

Answer 1

SLope = (2 - 7) / (-5 - 2) = 5/7

Equation of line: y - 7 = (5/7)(x - 2)

y = (5/7)x + (39/7)

7y = 5x + 39

So, 5x - 7y = -39

Answer 2

(2,7),(-5,2) have a line through them with slope = m = (7-2)/(2+5) = 5/7

line's equation is

y -7 = (5/7)(x-2) in point slope form

y = 5x/7 + 39/7 in slope intercept form

5x - 7y = -39 in standard form

5x-7y -39 = 0 in general form

an infinite number of equations for those two points for higher degree

Answer 3

To find the slope from two points, use the formula: m = (y₂-y₁)/(x₂-x₁)

With the given points (2, 7) and (−5, 2), we must first label them:

1. y₂ = 2
2. y₁ = 7
3. x₂ = -5
4. x₁ = 2

Now plugging these into our slope formula, we get: m = (2-7)/(-5-2)

Solving that: m = -5/-7

Since it is a negative divided by a negative, we get a positive. Two negatives = a positive, so the final slope would be: m = 5/7

The next step is to use the point slope formula: y-y₁ = m(x-x₁)

We only need to plug one of the two points into this equation. It does not matter which we use because both will give the same results. In this example, we will use (2,7):

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

You will now need to distribute the 5/7, so this means we will multiply 5/7 with x and -2 to get:

y-7=5/7x-10/7

Now, to get the y alone, we will need to add 7 to both the left and right side of the equation. The left side of the equation would cancel out. The right side, we will be adding 7 to -10/7. However, we cannot add a whole number to a fraction. Instead, we will have to convert 7 into a fraction that has the same denominator (the bottom number of the fraction). In this example, since the fraction we are are trying to add 7 to is -10/7, we will need to convert 7 into a fraction that has 7 as the denominator. In doing so, we can set up the following equation:

x/7 = 7

To solve for x, we would multiply 7 by 7 to get 49. Now we have a fraction with 7 as the common denominator: 49/7

Adding this to -10/7, gives you a result of:

39/7 because 49/7 + (-10/7) = 39/7

Since the line of an equation is y = mx + b, we now have the full equation:

y = 5/7x + 39/7