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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)