95.1k views
2 votes
Help please!What is the x-intercept of the line?X=33 Y=-22X=52 Y=-33X=71 Y=-44

User Hennson
by
2.7k points

1 Answer

5 votes

x intercept is -5

Step-by-step explanation

Step 1

find the slope of the line:

when you know 2 points of the line, you can find the slope, by using:


\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}

then,Let

P1(33,-22)

P2(52,-33)

replace,


\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(-33-(-22))/(52-33)=(-33+22)/(19)=(-11)/(19) \\ \text{slope}=-(11)/(19) \end{gathered}

Step 2

find the equation of the line


y-y_1=slope(x-x_1)\rightarrow equation

let


\begin{gathered} \text{slope}=-(11)/(19) \\ P1(33,-22) \end{gathered}

replace,


\begin{gathered} y-y_1=slope(x-x_1)\rightarrow equation \\ y-(-22)=-(11)/(19)(x-33) \\ y+22=-(11)/(19)x+(363)/(19) \\ to\text{ isolate y, subtract 22 in both sides} \\ y+22-22=-(11)/(19)x+(363)/(19)-22 \\ y=-(11)/(19)x-(55)/(19)\rightarrow equation\text{ of the line} \end{gathered}

now, we have the equation of the line, to get the x intercetp ( it is when y=0)

replace


\begin{gathered} y=-(11)/(19)x-(55)/(19)\rightarrow equation\text{ of the line} \\ 0=-(11)/(19)x-(55)/(19) \\ \text{isolate x} \\ (11)/(19)x=-(55)/(19) \\ 11x=-(55\cdot19)/(19) \\ 11x=-55 \\ \text{divide both sides by 11} \\ (11x)/(11)=(-55)/(11) \\ x=-5 \end{gathered}

so, the x intercetp is -5.

I hope this helps you

Help please!What is the x-intercept of the line?X=33 Y=-22X=52 Y=-33X=71 Y=-44-example-1
User Rjrjr
by
3.4k points