a. The line with equation y - 9 = -3/4(x - 4) has a slope of -3/4 and passes through the point (0, 12). b. The line with equation y = 3 - 2/3(x + 4) has a slope of -2/3 and passes through the point (-1/2, 0).
How to find the slope?
Let's find the slope and a point on the line for each given equation.
a. y - 9 = -3/4(x - 4)
First, let's rewrite the equation in the slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.
y - 9 = -3/4(x - 4)
Distribute the -3/4 on the right side:
y - 9 = -3/4x + 3
Add 9 to both sides to isolate y:
y = -3/4x + 12
Now we can identify the slope (m) and a point on the line. The slope is -3/4, and one point on the line is (0, 12).
b. y = 3 - 2/3(x + 4)
In this case, the slope (m) is -2/3, and the y-intercept (b) is 3. So, the slope is -2/3, and a point on the line is (-1/2, 0).