Question

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Answer 1

Answer:

When y = 0, x = -14

Thus, the x-intercept of the line is:

(x, y) = (-14, 0)

Step-by-step explanation:

From the table, taking two points

(-94, 24)

(-74, 18)

Finding the slope between (-94, 24) and (-74, 18)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-94,\:24\right),\:\left(x_2,\:y_2\right)=\left(-74,\:18\right)$

$m=\frac{18-24}{-74-\left(-94\right)}$

$m=-\frac{3}{10}$

We know the slope-intercept form of line equation is

$y = mx+b$

where m is the slope and b is the y-intercept

substituting m = -3/10 and the point (-94, 24) in the slope-intercept to determine the y-intercept 'b'

$24\:=\:-\frac{3}{10}\left(-94\right)+b$

$\frac{3}{10}\cdot \:94+b=24$

$\frac{141}{5}+b=24$

$b=-\frac{21}{5}$

now

substituting m = -3/10 and y-intercept 'b=-21/5' in the slope-intercept of line equation

$y = mx+b$

Thus, the equation of the line will be:

$\:y\:=\:-\frac{3}{10}x-\frac{21}{5}$

We know that the x-intercept can be determined by setting y = 0, and determining for x. so,

$\:0\:=\:-\frac{3}{10}x-\frac{21}{5}$

switch sides

$-\frac{3}{10}x-\frac{21}{5}=0$

$-\frac{3}{10}x=\frac{21}{5}$

$-3x=42$

divide both sides by -3

$\frac{-3x}{-3}=\frac{42}{-3}$

$x=-14$

so when y = 0, x = -14

Thus, the x-intercept of the line is:

(x, y) = (-14, 0)