Question

Find the equation of the line with x-intercept = 2 and y-intercept = -6. Write your answer in general form.

Answer 1

y=3x-6

Step-by-step 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:

`\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(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}`

we are given the intercepts ( also points of the line)

so

P1=(2,0)

P2=(0,-6)

replace

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(-6-0)/(0-2)=(-6)/(-2)=3 \end{gathered}`

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

`\begin{gathered} y=mx+b \\ \text{slope}=m=3 \\ b=y-\text{intercept}=-6 \\ \text{replacing} \\ y=3x-6 \end{gathered}`

so, the answer is

y=3x-6

I hope this helps you