Question

Find the value of x such that the line through the pair of points has the given slope:
(-1, 4) and (x, 5); m = -1/2

Answer 1

Answer:

x = -3

Step-by-step explanation:

Given the following points: (-1, 4) (x, 5); and the slope (m = -1/2):

We can use the point-slope formula to find the equation of the line:

$y - y_{1} = m(x - x_{1})$

Let  $(x_{1}, y_{1})$ = (-1, 4)

m = -1/2

Plug these values into the point-slope formula:

$y - y_{1} = m(x - x_{1})$

$y - 4 = - \frac{1}{2} (x - (-1))$

$y - 4 = - \frac{1}{2} (x + 1)$

$y - 4 = - \frac{1}{2}x - \frac{1}{2}$

Add 4 on both sides:

$y - 4 + 4 = - \frac{1}{2}x - \frac{1}{2} + 4$

The linear equation in slope-intercept form is:

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

Next, plug in the y-coordinate of the ordered pair, (x, 5) to solve for the missing x-cooridnate:

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

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

Subtract $\frac{7}{2}$ from both sides:

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

$\frac{3}{2} = -\frac{1}{2}x$

Divide both sides by $- \frac{1}{2}$ to solve for x:

$\frac{\frac{3}{2} }{-\frac{1}{2}} = \frac{-\frac{1}{2} x}{-\frac{1}{2}}$

-3 = x

Therefore, the missing x-coordinate of the ordered pair, (x , 5) is 3.