8th grade math problem 6

Question

Use the two points to write a slope-intercept equation. Then, transform it into Standard Form. (1,4) and (-5,-9)

Answer 1

Hi Nick, the first step is to find the slope using the two given points.

 

Slope:

 

Let m represent the slope.

 

m = (y₂ - y₁)/(x₂ - x₁), it does not matter which of the two points we assign to the (x₁, y₁), the result will be the same.

 

Let (1, 4) represent (x₁ , y₁) and (-5, -9) represent (x₂, y₂)

 

m = (-9 - 4)/(-5 -1)

 

m = -13/-6

 

m = 13/6

 

Point-slope form:

 

The point-slope form of a line is: y - y₁ = m * (x - x₁), again it does not matter which point we use. We will use the same (x₁, y₁) as before.

 

y - 4 = 13/6 * (x - 1)

 

Clear the fraction by multiplying the entire equation by 6:

 

6y - 24 = 13 * (x - 1)

 

6y - 24 = 13x - 13, we now have a line in the point-slope format.

 

Slope-intercept form:

 

y = m * x + b, where m is the slope and b is the y-component of the y-intercept point, (0, b).

 

6y - 24 = 13x - 13

 

6y = 13x + 11

 

y = 13/6 * x + 11/6, we now have the slope-intercept form of the line.

 

Standard form of a line:

 

Ax + By = C

 

To put the line in slope-intercept form into standard form, all that is necessary is to rearrange the terms.

 

y = 13/6 * x + 11/6

 

The standard form does not allow fractions:

 

Multiply the entire equation by 6 to clear the fractions:

 

6y = 13x + 11

 

Subtract 13x from both sides:

 

-13x + 6y = 11

 

Multiply the entire equation by -1 to make the x term positive:

 

13x - 6y = -11, this is the standard form of the line.

 

Check:

 

Substitute (1, 4) into the equation:

 

13 * 1 - 6 * 4 = -11

 

13 - 24 = -11

 

-11 = -11

 

Substitute (-5, -9) into the equation:

 

13 * -5 - 6 * -9 = -11

 

-65 + 54 = -11

 

-11 = -11

 

Values check.

 

Questions?