Question

What is an equation of the line that passes through the points (-6,5) and (6, 7)?

Answer 1

Answer:

$y = \frac{1}{6} x + 6$

Step-by-step explanation:

The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept. This form is known as the slope-intercept form.

Use the gradient formula below to find the value of m:

$gradient = \frac{y1 - y2}{x1 - x2}$

*(x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate.

$m = \frac{7 - 5}{6 - ( - 6)} \\ m = \frac{2}{12} \\ m = \frac{1}{6}$

Substitute the value of m into the equation:

y= ⅙x +c

To find the value of c, substitute a pair of coordinates.

When x= 6, y= 7,

$7 = \frac{1}{6} (6) + c \\ 7 = 1 + c \\ c = 7 - 1 \\ c = 6$

Thus, the equation of the line is y= ⅙x +6.