Ben 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 = -10x + 20
y=-2x + 20
He concluded that the y-intercept is (0, 20).
Part A: What error did Ben make? (2 points)
Part B: What are the x- and y-intercepts of the line? Explain or show your reasoning.

To find the y intercept, plug in x = 0 to determine that y = 5. The (-5/2)x part goes away since it goes to 0. Therefore, the y intercept is located at (0,5).

To find the x intercept, plug in y = 0 to find x. You can use the original equation or the equation we just found. I think the original equation is easier to work with in this case.

10x + 4y = 20

10x + 4*0 = 20

10x = 20

x = 20/10

x = 2

We have x = 2 pair up with y = 0; therefore the x intercept is located at (2,0)

--------------------------------------------------------------------------

Summary:

Part A: Ben made a mistake on his 3rd line. He didn't divide both sides by 4 correctly.
Part B: x and y intercepts are located at (2,0) and (0,5) respectively

semsee45 semsee45 · Answer 2 · 2024-02-10T22:57:30+01:00

Answer:

A) Ben did not correctly divide both sides of the equation by 4.

B) x-intercept = (2, 0)
y-intercept = (0, 5)

Step-by-step explanation:

The intercepts are the points at which the line crosses or intersects the coordinate axes.

Part A

Ben made an error in isolating the y-variable. While he correctly subtracted 10x from both sides of the equation, his next step should have been to divide both sides by 4. He did this correctly on the left side of the equation, but incorrectly on the right side. Therefore, his conclusion that the y-intercept is (0, 20) is also incorrect.

Part B

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To correctly put the equation in slope-intercept form, begin by subtracting 10x from both sides of the equation:

[tex]10x+4y-10x=-10x+20\\\\4y=-10x+20[/tex]

Now, divide both sides of the equation by 4:

[tex]\dfrac{4y}{4}=\dfrac{-10x}{4}+\dfrac{20}{4}\\\\\\y=-\dfrac{5}{2}x+5[/tex]

Therefore, the slope of the line is -5/2 and the y-intercept is (0, 5).

The x-intercept is the point at which the line crosses or intersects the x-axis, so when y = 0. Therefore, the find the x-intercept, substitute y = 0 into the equation and solve for x:

[tex]0=-\dfrac{5}{2}x+5\\\\\\\dfrac{5}{2}x=5\\\\\\\dfrac{5}{2}x\cdot 2=5\cdot 2\\\\\\5x=10\\\\\\\dfrac{5x}{5}=\dfrac{10}{5}\\\\\\x=2[/tex]

Therefore, the x-intercept is (2, 0).