Question

Need help writing the equation of the line in fully simplified slope-intercept form

Answer 1

y=4x-5

Explanation

the slope -intercept form of the equation of a line is

$\begin{gathered} y=mx+b \\ where\text{ m is the slope and b is the y-intercept} \end{gathered}$

so

Step 1

find the slope of the line

we can find the slope of a line using the formula

$\begin{gathered} slope=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2)\text{ are 2 points from the line} \end{gathered}$

so

a) let

$\begin{gathered} P1(-1,-1) \\ P2(0,-5) \end{gathered}$

b) now, replace in the formula

$\begin{gathered} slope\frac{}{}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{-5-(-1)}{0-(-1)}=\frac{-5+1}{1}=-4 \end{gathered}$

Step 2

y-intercept:

now, to find the value of b ( y-intercpet) we need to check in the graph , the point where the lines crosses the y-axis and take the y-coordinate, so

so

b=-5

Step 3

finally, replace

$\begin{gathered} y=mx+b \\ y=-4x-5 \end{gathered}$

so, the equation of the line is

y=-4x-5