Respuesta :

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)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-94,\:24\right),\:\left(x_2,\:y_2\right)=\left(-74,\:18\right)[/tex]

[tex]m=\frac{18-24}{-74-\left(-94\right)}[/tex]

[tex]m=-\frac{3}{10}[/tex]

We know the slope-intercept form of line equation is

[tex]y = mx+b[/tex]

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'

[tex]24\:=\:-\frac{3}{10}\left(-94\right)+b[/tex]

[tex]\frac{3}{10}\cdot \:94+b=24[/tex]

[tex]\frac{141}{5}+b=24[/tex]

[tex]b=-\frac{21}{5}[/tex]

now

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

[tex]y = mx+b[/tex]

Thus, the equation of the line will be:

[tex]\:y\:=\:-\frac{3}{10}x-\frac{21}{5}[/tex]

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

[tex]\:0\:=\:-\frac{3}{10}x-\frac{21}{5}[/tex]

switch sides

[tex]-\frac{3}{10}x-\frac{21}{5}=0[/tex]

[tex]-\frac{3}{10}x=\frac{21}{5}[/tex]

[tex]-3x=42[/tex]

divide both sides by -3

[tex]\frac{-3x}{-3}=\frac{42}{-3}[/tex]

[tex]x=-14[/tex]

so when y = 0, x = -14

Thus, the x-intercept of the line is:

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

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