Respuesta :
y=3x-6
Explanation
the equation of a lines is given bne
where m is the slope and b is the y-intercept
so
Step 1
the slope of a line si given by:
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where P1(x}_1,y_1) \\ \text{and P2(x}_2,y_2) \\ \text{are 2 known points from the line} \end{gathered}[/tex]we are given the intercepts ( also points of the line)
so
P1=(2,0)
P2=(0,-6)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-6-0}{0-2}=\frac{-6}{-2}=3 \end{gathered}[/tex]so,the slope of the line is 3
Step 2
now, we have the slope and the given y-intercept, we can replace in the equation of the line
[tex]\begin{gathered} y=mx+b \\ \text{slope}=m=3 \\ b=y-\text{intercept}=-6 \\ \text{replacing} \\ y=3x-6 \end{gathered}[/tex]so, the answer is
y=3x-6
I hope this helps you
