Question

Write the equation of line that passes through (-1,3) and (-5,-3)

Answer 1

Answer:

$y = \frac{3}{2} x + 4 \frac{1}{2}$

Step-by-step explanation:

y=mx+c

where m is the gradient and c is the y-intercept of the line

Let's find the gradient of the line first.

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

Using the above formula,

$gradient \: of \: line \\ = \frac{3 - ( - 3)}{ - 1 - ( - 5)} \\ = \frac{3 + 3}{5 - 1} \\ = \frac{6}{4} \\ = \frac{3}{2}$

Subst. the gradient into m:

$y = \frac{3}{2} x + c$

Now, find the value of c by substituting a coordinate into the above equation.

when x=-1, y=3,

$3 = \frac{3}{2} ( - 1) + c \\ 3 = -\frac{3}{2} + c \\ c = 3 + \frac{3}{2} \\ c = 4 \frac{1}{2}$

Therefore the equation of the line is

$y = \frac{3}{2} x + 4\frac{1}{2}$