To find the x-intercept and y-intercept of the line $8y = -6x + 20$, we follow these steps:

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1. Find the x-intercept

The x-intercept is the point where the line crosses the x-axis, i.e., when $y = 0$.

Substitute $y = 0$ into the equation:

$8(0) = -6x + 20$

Simplify:

$0 = -6x + 20$

Solve for $x$:

$6x = 20 \quad \Rightarrow \quad x = \frac{20}{6} = \frac{10}{3}$

Thus, the x-intercept is:

$\boxed{\left(\frac{10}{3}, 0\right)}$

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2. Find the y-intercept

The y-intercept is the point where the line crosses the y-axis, i.e., when $x = 0$.

Substitute $x = 0$ into the equation:

$8y = -6(0) + 20$

Simplify:

$8y = 20$

Solve for $y$:

$y = \frac{20}{8} = \frac{5}{2}$

Thus, the y-intercept is:

$\boxed{\left(0, \frac{5}{2}\right)}$

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Final Answer:

• x-intercept: $\left(\frac{10}{3}, 0\right)$
• y-intercept: $\left(0, \frac{5}{2}\right)$

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Would you like me to graph this line or provide further details? 😊

Related Questions:

1. How do you determine the slope of the line from the equation $8y = -6x + 20$?
2. What is the slope-intercept form of $8y = -6x + 20$?
3. How do you rewrite $8y = -6x + 20$ in standard form?
4. Can you verify the intercepts using another form of the equation?
5. How would you solve for intercepts if the equation were in another form, like $y = mx + b$?

Tip:

Always double-check your calculations by substituting the intercept values back into the original equation to ensure they satisfy it.