Answer:
[tex]y = \frac{1}{6} x + 6[/tex]
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:
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
*(x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate.
[tex]m = \frac{7 - 5}{6 - ( - 6)} \\ m = \frac{2}{12} \\ m = \frac{1}{6} [/tex]
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,
[tex]7 = \frac{1}{6} (6) + c \\ 7 = 1 + c \\ c = 7 - 1 \\ c = 6[/tex]
Thus, the equation of the line is y= ⅙x +6.
