Final answer:
To express the equation y - 6 = -3/4(x - 6) in slope-intercept form (y = mx + b), distribute the slope -3/4 and then isolate y, resulting in y = -3/4x + 21/2.
Step-by-step explanation:
To write the equation y - 6 = -3/4(x - 6) in the form y = mx + b, we need to solve for y by isolating it on one side of the equation. Start by distributing the slope -3/4 to the terms inside the parentheses:
y - 6 = -3/4x + 3/4 × 6
Let's simplify the right side:
y - 6 = -3/4x + 9/2
Next, add 6 to both sides to get y by itself:
y = -3/4x + 9/2 + 6
Now, find a common denominator to combine the terms on the right:
y = -3/4x + 9/2 + 12/2
Combine the constant terms:
y = -3/4x + 21/2
We now have the equation in slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept.