Question

2

Answer 1

Answer:

Part 1) x-intercept is -4;y-intercept is 8

Part 2) x-intercept is 16; y-intercept is 20

Part 3) $x+6y=24$

Part 4)

Part a) $4.75k+2.25p=22$

Part b) The graph in the attached figure

Step-by-step explanation:

Part 1) Find the x- and y-intercept of the line

we have

$-10x+5y = 40$

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$-10x+5(0) = 40$

$-10x=40$

$x=-4$

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

$-10(0)+5y = 40$

$5y = 40$

$y=8$

therefore

x-intercept is -4;y-intercept is 8

Part 2) Find the x- and y-intercept of the line

we have

$5x+4y=80$

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$5x+4(0)=80$

$5x=80$

$x=16$

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

$5(0)+4y=80$            

$4y=80$

$y=20$              

therefore

x-intercept is 16; y-intercept is 20

Part 3) Write y=-(1/6)x+4 in standard form using integers.

we know that

The equation of a line in standard form is equal to

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=-\frac{1}{6}x+4$

Multiply both sides by 6 to remove the fraction

$6y=-x+24$

Adds x both sides

$x+6y=24$

Part 4) The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound.

Part a) Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22

Part b) Graph the equation

Part a)

Let

k -----> the number of pounds of kumquats bought

p ----> the number of pounds of Asian pears bough

we know that

The number of pounds of kumquats bought (k) multiplied by it cost of $4.75 a pound plus the number of pounds of Asian pears bough (p) multiplied by it cost of $2.25 a pound must be equal to $22

so

$4.75k+2.25p=22$

Part b) Graph the equation

To graph the line find out the intercepts

Let

k the first coordinate of the point

p the second coordinate of the point

The k-intercept is the value of k when the value of p is equal to zero

so

For p=0

$4.75k+2.25(0)=22$

$4.75k=22$

$k=4.63$

so

The k-intercept is the point (4.63,0)

The p-intercept is the value of p when the value of k is equal to zero

so

For k=0

$4.75(0)+2.25p=22$

$2.25p=22$

$p=9.78$

so

The k-intercept is the point (0,9.78)

using a graphing tool

Plot the intercepts and join the points to graph the line

see the attached figure

Remember that the weight cannot be a negative number