Question

.___________________.
.___________________.

Answer 1

When y = 0, x = -14

Thus, the x-intercept of the line is:

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

Explanation:

From the table, taking two points

(-94, 24)

(-74, 18)

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

`\mathrm{Slope}=(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=(18-24)/(-74-\left(-94\right))`

`m=-(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\:=\:-(3)/(10)\left(-94\right)+b`

`(3)/(10)\cdot \:94+b=24`

`(141)/(5)+b=24`

`b=-(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\:=\:-(3)/(10)x-(21)/(5)`

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

`\:0\:=\:-(3)/(10)x-(21)/(5)`

switch sides

`-(3)/(10)x-(21)/(5)=0`

`-(3)/(10)x=(21)/(5)`

`-3x=42`

divide both sides by -3

`(-3x)/(-3)=(42)/(-3)`

`x=-14`

so when y = 0, x = -14

Thus, the x-intercept of the line is:

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