Question

Write the linear equation in slope-intercept form passing through the point with the given slope. (2,3); slope = -4

a. y = -4x - 5
b. y = -4x + 11
c. y = 4x - 5
d. y = 4x + 11

Answer 1

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.