Question

This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
48 -30
61 -45
74 -60
What is the x-intercept of the line?

Answer 1

Answer:

22

Step-by-step explanation:

First, find the equation of the line in slope-intercept form, y = mx + b.

Using the coordinates of these two pairs, (48, -30) and (61, -45), the slope (m) can be calculated as follows:

$m = \frac{y_2 - y_2}{x_2 - x_1} = \frac{-45 -(-30)}{61 - 48} = \frac{-15}{13}$

$slope (m) = -\frac{15}{13}$

Find the y-intercept (b) by substituting x = 48, y = -30, and $m = -\frac{15}{13}$ into y = mx + b:

$-30 = -\frac{15}{13}(48) + b$

Solve for b.

$-30 = -\frac{720}{13} + b$

Add $-\frac{720}{13}$ to both sides

$-30 + \frac{720}{13} = b$

$\frac{-390 + 720}{13} = b$

$\frac{330}{13} = b$

$b = \frac{330}{13}$

Substitute $m = -\frac{15}{13}$ and $b = \frac{330}{13}$ into y = mx + b

$y = -\frac{15}{13}x + \frac{330}{13}$

The x-intercept of the line with the above equation, would be the value of x when y = 0. This is the value of x where the line cuts across the x-axis. To calculate this, substitute y = 0 into $y = -\frac{15}{13}x + \frac{330}{13}$.

$0 = -\frac{15}{13}x + \frac{330}{13}$

Subtract $\frac{330}{13}$ from both sides

$-\frac{330}{13} = -\frac{15}{13}x$

Divide both sides by $-\frac{13}{15}x$

$\frac{-\frac{330}{13}}{-\frac{13}{15}} = x$

$-\frac{330}{13}*-\frac{13}{15} = x$

$-\frac{330}{1}*-\frac{1}{15} = x$

$\frac{330}{15} = x$

$22 = x$

The x-intercept = 22

Answer 2

Answer:

(22,0)

Step-by-step explanation: