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ine
p contains the points
(-1,2) and
(2,11) in the
xy oordinate plane.
What are two other points that lie on the line
p ?
A.
(-3,-4) and
(1,9)
B.
(0,-5) and
(-1,8)
C.
(-1,9) and
(3,4)
D.
(0,5) and
(1,8)

ine $p$ contains the points $(-1,2)$ and $(2,11)$ in the $x y$ oordinate plane. $\newline$ What are two other points that lie on the line $p$ ? $\newline$ A. $(-3,-4)$ and $(1,9)$ $\newline$ B. $(0,-5)$ and $(-1,8)$ $\newline$ C. $(-1,9)$ and $(-1,2)$ $0$ $\newline$ D. $(-1,2)$ $1$ and $(-1,2)$ $2$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. ine

p

contains the points

(-1,2)

and

(2,11)

in the

x y

oordinate plane.

\newline

What are two other points that lie on the line

p

?

\newline

A.

(-3,-4)

and

(1,9)

\newline

B.

(0,-5)

and

(-1,8)

\newline

C.

(-1,9)

and

(-1,2)

0

\newline

D.

(-1,2)

1

and

(-1,2)

2

Calculate slope: Calculate the slope of the line using the points $(-1,2)$ and $(2,11)$ . Slope $(m) = \frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{(11 - 2)}{(2 - (-1))} = \frac{9}{3} = 3.$
Use point-slope form: Use the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$ , substituting $m = 3$ and point $(-1,2)$ . $y - 2 = 3(x + 1)$ .
Simplify equation: Simplify the equation to get the slope-intercept form, $y = 3x + 5$ .
Check point $(-3,-4)$ : Check if the point $(-3,-4)$ satisfies the equation $y = 3x + 5$ . Substitute $x = -3$ into the equation: $y = 3(-3) + 5 = -9 + 5 = -4$ .
Check point $(1,9)$ : Check if the point $(1,9)$ satisfies the equation $y = 3x + 5$ . Substitute $x = 1$ into the equation: $y = 3(1) + 5 = 3 + 5 = 8$ .

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