Find the x and y-intercepts of the following equation:

Question

5x + 2y = 10
•x-intercept (5, 0)
x-intercept (2,10) y-intercept (0, 5) y-intercept (0,2)

Answer 1

To find the x-intercept and y-intercept of the equation $5x+2y=10$, we can follow these steps:

Finding the x-intercept:

The x-intercept occurs where $y=0$.

Substituting $y=0$ into the equation: $$5x+2(0)=10$$ $$5x=10$$ $$x=\frac{10}{5}=2$$

Thus, the x-intercept is $(2,0)$.

Finding the y-intercept:

The y-intercept occurs where $x=0$.

Substituting $x=0$ into the equation: $$5(0)+2y=10$$ $$2y=10$$ $$y=\frac{10}{2}=5$$

Thus, the y-intercept is $(0,5)$.

Summary:

• The x-intercept is $(2,0)$.
• The y-intercept is $(0,5)$.

From the options provided, the correct intercepts are:

• x-intercept: $(2,0)$
• y-intercept: $(0,5)$