Question

A line passes through (10,2) and (14,-22). Write the equation of the line in standard form.

Answer 1

Answer:

The equation of the line in standard form is:

$6x + y = 62$

Step-by-step explanation:

Given the points

• (10,2)

• (14,-22)

Determining the slope between (10, 2) and (14, -22)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(10,\:2\right),\:\left(x_2,\:y_2\right)=\left(14,\:-22\right)$

$m=\frac{-22-2}{14-10}$

$m=-6$

The point-slope form of the line equation is  

$y-y_1=m\left(x-x_1\right)$

where

• m is the slope of the line

• (x₁, y₁) is the point

substituting the values m = -6 and the point (10, 2) in the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

$y - 2 = -6(x - 10)$

$y - 2 = -6x +60$

adding 2 to both sides

$y-2+2 = -6x + 60 + 2$

$y = -6x + 62$

We can write the equation in the standard form such as

Ax + By = C

Thus,

$y = -6x + 62$

adding -6x to both sides

$6x + y = -6x + 62 + -6x$

$6x + y = 62$

Therefore, the equation of the line in standard form is:

$6x + y = 62$