Question

b. \\(y = 2x - 6\\)

\\(y\text{ int} = (x = 0)\\)
\\(y = 2(0) - 6\\)
\\(y = -6\\)
\\((0, -6) \longleftrightarrow y\text{ intercept}\\)

\\(x\text{ int} (y = 0)\\)
\\((0) = 2x - 6\\)
\\(6 = 2x\\)
\\(x = 3\\)
\\((3, 0) \longleftrightarrow x\text{ intercept}\\)

Explanation:

Find the y-intercept

To find the y-intercept, set \(x = 0\) in the equation.

$$ y = 2(0) - 6 = -6 $$

The y-intercept is at \((0, -6)\).

Find the x-intercept

To find the x-intercept, set \(y = 0\) in the equation.

$$ 0 = 2x - 6 $$

Solve for \(x\):

$$ 2x = 6 \implies x = 3 $$

The x-intercept is at \((3, 0)\).

Plot the intercepts and draw the line

Plot the points \((0, -6)\) and \((3, 0)\) on the coordinate plane.
Draw a straight line passing through both points to represent \(y = 2x - 6\).

Answer:

The linear equation is \(y = 2x - 6\).

• y-intercept: \((0, -6)\)
• x-intercept: \((3, 0)\)

The graph is a straight line passing through these two points.