Question

determine the intercepts of the line. do not round your answers. y = -3x + 12 y-intercept: (□, □) x-intercept: (□, □) your answer should be • an integer, like 6 • a simplified proper fraction, like 3/5 • a simplified improper fraction, like 7/4

Explanation:

Step1: Find y-intercept (set x=0)

To find the y - intercept, we set \( x = 0 \) in the equation \( y=-3x + 12 \). Substituting \( x = 0 \) into the equation, we get \( y=-3(0)+12 \). Simplifying this, \( y = 0 + 12=12 \). So the y - intercept is at the point \( (0,12) \).

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

To find the x - intercept, we set \( y = 0 \) in the equation \( y=-3x + 12 \). So we have the equation \( 0=-3x + 12 \). First, we add \( 3x \) to both sides of the equation to get \( 3x=12 \). Then, we divide both sides by 3: \( x=\frac{12}{3}=4 \). So the x - intercept is at the point \( (4,0) \).

Answer:

y - intercept: \( (0, 12) \)
x - intercept: \( (4, 0) \)