Question: 6. For the equation \( y = 3x - 6 \) a. Find the \( x \)-intercept of the line. \( y = 0 \)…

6. For the equation \( y = 3x - 6 \)

a. Find the \( x \)-intercept of the line.

\( y = 0 \) and solve for \( x \)

b. Find the \( y \)-intercept of the line.

\( x = 0 \) and solve for \( y \)

c. Sketch the line using the \( x \)- and \( y \)-intercept.

[Graph grid]

6A

Solution

For the equation \( y = 3x - 6 \): a. Find the x-intercept of the line. To find the x-intercept, set \( y = 0 \) and solve for \( x \). \[ 0 = 3x - 6 \] Add 6 to both sides: \[ 6 = 3x \] Divide both sides by 3: \[ x = 2 \] The x-intercept is \( (2, 0) \). b. Find the y-intercept of the line. To find the y-intercept, set \( x = 0 \) and solve for \( y \). \[ y = 3(0) - 6 \] \[ y = -6 \] The y-intercept is \( (0, -6) \). c. Sketch the line using the x- and y-intercept. Plot the points \( (2, 0) \) and \( (0, -6) \) on the graph and draw a line through them.