Mathematics, 06.06.2020 11:57 dkdk31

Question 7 The equation of a straight line AB is

(a) Find the gradient of line AB.
(b) Find the y-intercept of line AB.
(c) A second line PQ is parallel to the line AB and passes through a point (2, -8).
Show that the second line PQ also passes through the point(-1,-5)

$\frac{x}{2} + \frac{y}{2} = 1$

Answers: 3

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Answer from: kylemartinez13

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

$\frac{x}{2}$ + $\frac{y}{2}$ = 1 ( multiply through by 2 to clear the fractions )

x + y = 2 ( subtract x from both sides )

y = - x + 2 ← in slope- intercept form

(a) with slope m = - 1

(b) with y- intercept c = 2

(c)

Parallel lines have equal slopes, thus

y = - x + c ← is the partial equation of PQ

To find c substitute (2, - 8) into the partial equation

- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6

y = - x - 6 ← equation of PQ

To show (- 1, - 5) lies on PQ, substitute x = - 1 into the equation and evaluate for y.

y = - (- 1) - 6 = 1 - 6 = - 5 ← the given y- coordinate

Thus PQ passes through (- 1, - 5 )

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at ( h , k ) .

center: ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center: ( 3 , 1 ).

radius: 4

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Question 7 The equation of a straight line AB is

(a) Find the gradient of line AB...