Question

Han wanted to find the intercepts of the graph of the equation 10x + 4y = 20. He decided to put the equation in slope-intercept form first. Here is his work 10x + 4y = 20 4y = 20 - 10x y = 5 - 10x He concluded that the x-intercept is (,0) and the v-intercept is (0. 5). a. What error did Han make? b. What are the x- and y-intercepts of the line? Explain or show your reasoning.

Answer 1

see explanation

Explanation:

(a)

from his work he has

4y = 20 - 10x ( which is correct ) , then

y = 5 - 10x ( error here )

he has not divided completely through by 4 , he should have

y = 5 -
`(5)/(2)` x

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(b)

given the equation

10x + 4y = 20

the x- intercept is the point on the x- axis where the line crosses.

the y- coordinate of any point on the x- axis is zero

substitute y = 0 into the equation and solve for x

10x + 4(0) = 20

10x + 0 = 20

10x = 20 ( divide both sides by 10 )

x = 2 ← x- intercept or (2, 0 ) in coordinate form

the y- intercept is the point on the y- axis where the line crosses.

the x- coordinate of any point on the y- axis is zero

substitute x = 0 into the equation and solve for y

10(0) + 4y = 20

0 + 4y = 20

4y = 20 ( divide both sides by 4 )

y = 5 ← y- intercept or (0, 5 ) in coordinate form