Question

Find the equation of the line
passing through the points (3,1) and (7,-7)

Answer 1

Answer:

y = -2x+7

Step-by-step explanation:

equation of line formula:

$y = mx + c$

m = slope, c = y-intercept

1) find the slope using the given coordinates

slope formula:

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

i) (3,1)

x1=3

y1=1

ii) (7,-7)

x2=7

y2=-7

substitute the values into the formula

$m = \frac{ - 7 - 1}{7 - 3}$

$m = \frac{ - 8}{4}$

$m = - 2$

so now half of the equation is complete as we have the the value of m. substitute the value of m into the slope formula.

$y = - 2x + c$

2) find the value of c

to find the value of c, we must substitute either coordinate into the half equation. so, i choose the coordinate (3,1). if you substitute the coordinate (7,-7) , you will get the same value of c.

(3,1)

x = 3

y = 1

$y = - 2x + c$

$1 = - 2(3) + c$

$1 = - 6 + c$

$1 + 6 = c$

$c = 7$

substitute the value of c into the half equation and that is your straight line equation

$y = - 2x + 7$