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) $y - 9 = -2(x - 4)$
b) $y + 1 = \frac{1}{2}(x - 5)$
c) $y - 8 = -\frac{3}{4}(x + 12)$

Explanation:

Step1: Expand right-hand side

$y-9=-2x+8$

Step2: Isolate $y$

$y=-2x+8+9$
$y=-2x+17$

Step3: Identify slope & y-intercept

Slope $m=-2$, y-intercept $b=17$

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Step1: Expand right-hand side

$y+1=\frac{1}{2}x-\frac{5}{2}$

Step2: Isolate $y$

$y=\frac{1}{2}x-\frac{5}{2}-1$
$y=\frac{1}{2}x-\frac{7}{2}$

Step3: Identify slope & y-intercept

Slope $m=\frac{1}{2}$, y-intercept $b=-\frac{7}{2}$

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Step1: Expand right-hand side

$y-8=-\frac{3}{4}x-9$

Step2: Isolate $y$

$y=-\frac{3}{4}x-9+8$
$y=-\frac{3}{4}x-1$

Step3: Identify slope & y-intercept

Slope $m=-\frac{3}{4}$, y-intercept $b=-1$

Answer:

a) Equation: $y=-2x+17$; Slope: $-2$; y-intercept: $17$
b) Equation: $y=\frac{1}{2}x-\frac{7}{2}$; Slope: $\frac{1}{2}$; y-intercept: $-\frac{7}{2}$
c) Equation: $y=-\frac{3}{4}x-1$; Slope: $-\frac{3}{4}$; y-intercept: $-1$