Question

3
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 $\left(\frac{1}{2}, 0\
ight)$ and the $y$-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.

Explanation:

Step1: Identify Han's algebraic error

When isolating $y$, Han divided $20$ by $4$ to get $5$ but failed to divide $-10x$ by $4$. The correct step after $4y=20-10x$ is dividing all terms by 4.
Expression: $y=\frac{20}{4}-\frac{10x}{4}=5-\frac{5}{2}x$

Step2: Find x-intercept (set y=0)

Set $y=0$ in the original equation $10x+4y=20$, solve for $x$.
Expression: $10x + 4(0)=20 \implies 10x=20 \implies x=2$

Step3: Find y-intercept (set x=0)

Set $x=0$ in the original equation $10x+4y=20$, solve for $y$.
Expression: $10(0) + 4y=20 \implies 4y=20 \implies y=5$

Answer:

a. Han did not divide the $-10x$ term by 4 when isolating $y$; he only divided the constant term 20 by 4.
b. The x-intercept is $(2, 0)$ and the y-intercept is $(0, 5)$.