Questions: Fill in the table with this relationship's intercepts: 4y=30-15x

Transcript text: 4 Fill in the table with this relationship's intercepts: $4 y=30-15 x$

Solution

Solution Steps

To find the intercepts of the given linear equation, we need to determine where the line crosses the x-axis and y-axis. For the x-intercept, set $ y = 0 $ and solve for $ x $. For the y-intercept, set $ x = 0 $ and solve for $ y $.

Step 1: Find the x-intercept

To find the x-intercept, we set $ y = 0 $ in the equation $ 4y = 30 - 15x $. This gives us: \[ 4(0) = 30 - 15x \implies 0 = 30 - 15x \implies 15x = 30 \implies x = 2 \] Thus, the x-intercept is $ (2, 0) $.

Step 2: Find the y-intercept

To find the y-intercept, we set $ x = 0 $ in the equation $ 4y = 30 - 15x $. This results in: \[ 4y = 30 - 15(0) \implies 4y = 30 \implies y = \frac{30}{4} = \frac{15}{2} \] Thus, the y-intercept is $ \left(0, \frac{15}{2}\right) $.

Final Answer

The intercepts of the relationship are:

x-intercept: $ \boxed{(2, 0)} $
y-intercept: $ \boxed{\left(0, \frac{15}{2}\right)} $

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