Question

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:$10x + 4y = 20LXB0y = 5 - 10x$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 error

When isolating $y$, Han divided only the constant term by 4, not the $x$-term.
Original manipulation error: $4y=20-10x$ → $y=5-10x$ (incorrect; should divide all terms by 4)

Step2: Correct slope-intercept form

Divide every term by 4 to solve for $y$.
$$y=\frac{20}{4}-\frac{10x}{4}=5-\frac{5}{2}x$$

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

Set $y=0$ and solve for $x$.
$$0=5-\frac{5}{2}x$$
$$\frac{5}{2}x=5$$
$$x=5\times\frac{2}{5}=2$$

Step4: Find y-intercept (set x=0)

Set $x=0$ and solve for $y$.
$$y=5-\frac{5}{2}(0)=5$$

Answer:

a. Han failed to divide the $-10x$ term by 4 when isolating $y$.
b. x-intercept: $(2, 0)$; y-intercept: $(0, 5)$