Question

express each of the equations in the form y = mx + b. then, determine the slope and the y-intercept of each of the lines.
a) 4x + 2y - 6 = 0
b) x - 3y - 9 = 0

Explanation:

Step1: Isolate the y-term

$2y = -4x + 6$

Step2: Solve for y (divide by 2)

$y = \frac{-4x + 6}{2} = -2x + 3$

Step3: Identify slope and intercept

Slope $m=-2$, y-intercept $b=3$

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Step1: Isolate the y-term

$-3y = -x + 9$

Step2: Solve for y (divide by -3)

$y = \frac{-x + 9}{-3} = \frac{1}{3}x - 3$

Step3: Identify slope and intercept

Slope $m=\frac{1}{3}$, y-intercept $b=-3$

Answer:

a) Rewritten form: $y = -2x + 3$; Slope: $-2$, y-intercept: $(0, 3)$
b) Rewritten form: $y = \frac{1}{3}x - 3$; Slope: $\frac{1}{3}$, y-intercept: $(0, -3)$