Question

this table gives a few (x,y) pairs of a line in the coordinate plane.

x y
33 -22
52 -33
71 -44

what is the x - intercept of the line?

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intercepts from a table

Explanation:

Step1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(33,-22)$ and $(x_2,y_2)=(52,-33)$. Then $m=\frac{-33+22}{52 - 33}=\frac{-11}{19}$.

Step2: Use the point - slope form to find the equation of the line

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(33,-22)$ and $m =-\frac{11}{19}$, we have $y+22=-\frac{11}{19}(x - 33)$.

Step3: Find the x - intercept

The x - intercept is found by setting $y = 0$. So, $0+22=-\frac{11}{19}(x - 33)$. First, simplify the equation: $22=-\frac{11}{19}(x - 33)$. Multiply both sides by $- \frac{19}{11}$: $22\times(-\frac{19}{11})=x - 33$. Then $- 38=x - 33$. Solve for $x$: $x=-5$.

Answer:

$-5$