Final answer:
Using the point (2, 3) and the slope -4, the y-intercept b is calculated to be 11, resulting in the linear equation y = -4x + 11.
Step-by-step explanation:
To write the linear equation in slope-intercept form that passes through a specific point with a given slope, we can use the formula y = mx + b, where m is the slope, and b is the y-intercept. In this case, we know the slope (m) is -4, and the equation needs to pass through the point (2, 3). We can substitute the slope and the coordinates of the point into the equation and solve for b.
y = mx + b
3 = (-4)(2) + b
3 = -8 + b
b = 3 + 8
b = 11
The y-intercept (b) is 11. Now, we can write the final equation with the slope -4 and the y-intercept 11:
y = -4x + 11
Looking at the options provided, the correct equation is (b) y = -4x + 11.