Question

Write the equation of the line that passes through the two points:
(-4, 11) and (2,-4)

Answer 1

Answer:

y= -$\frac{5}{2}$x+1

Step-by-step explanation:

Utilize the formula of $\frac{y2-y1}{x2-x1}$ to find the distance between two points, or in this case, the equation of the line that passes through two points.

Applying the given points to identify the slope

1. Plug the coordinates into the y and x values. $\frac{-4-11}{2+4}$=-$\frac{15}{6}$.

1.5. Simplify; divide both the numerator and the denominator by 3. -$\frac{5}{2}$.

Applying slope and a point to find the y-intercept of the equation of a line

1. Utilize the formula of y=mx. Though this sounds strange, morph the sign of equality into subtraction.

1.5. Result: y-mx

2. Do this for both points.

First point: (-4,11)

y-mx

11 + $\frac{5}{2}$ (-4)

11 + -10 (11-10)

1

Plug the result and the slope into y=mx+b to find the slope of the line.

Result: y=-$\frac{5}{2}$x+1.

Check your answer to confirm that the value of y is true for both points

1. Do the same thing you did with the first point, but use the second point this time.

2.

y-mx

-4 + $\frac{5}{2}$ (2)

-4 + 5

1

Plug the result and the slope into y=mx+b to find the slope of the line.

Result: y=-$\frac{5}{2}$x+1. Identical to point one's result.

In conclusion, both of the results are the same. Therefore, the equation of the line must be y=-$\frac{5}{2}$x+1.