Question

What is an equation of the line that passes through the points (4,-6) and (8,-4)​

Answer 1

Answer:

$y = \frac{1}{2} x - 8$

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient (also known as slope) and c is the y-intercept (the point through which the line cuts through the y-axis).

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

Using the gradient formula above,

$m = \frac{ -4 - ( - 6)}{8 - 4} \\ m = \frac{ - 4 + 6}{4} \\ m = \frac{2}{4} \\ m = \frac{1}{2}$

Substitute the value of m into the equation:

y= ½x +c

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

When x=4, y= -6,

-6= ½(4) +c

-6= 2 +c

c= -6 -2 (-2 on both sides)

c= -8 (simplify)

Thus, the equation of the line is y= ½x -8.