Question

Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5

Answer 1

Answer:

It is y = x - 5

Step-by-step explanation:

General equation of a line:

${ \bf{y = mx + c}}$

m is the gradient, and c is y-intercept.

For gradient:

$slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}}$

substitute:

$slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1$

m = 1

for y-intercept:

consider point (6, 1):

$y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5$

therefore:

${ \sf{equation \: is \: \{y = x - 5 \}}}$