Find the equation of the following lines:
(I) The line with a slope of -8 and a y-intercept of 3. Express the equation in slope-intercept form.
(II) The line that passes through (-2,0) and has a slope of 5. Express the equation is point-slope form.
(III) The horizantal line that passes through (-2,6).
(IV) The vertical llne that passes through (-2,6).

Expert Answers

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(I) Slope is -8 and y-intercept is 3.
The slope-intercept form of a line is

`y=mx+b` ,

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

Hence, the equation of the given line in slope-intercept form is `y=-8x+3` .

(II) Passes the point (-2,0) and has a slope of 5.
The point-slope form of a line is

`y-y_1=m(x-x_1)`

where m is the slope and (x1,y1) is one of the given points

Substituting m=5, x1=-2 and y=0 to the formula yields:

`y-0=5(x-(-2))`

`y=5(x+2)`

Hence, the equation of the given line in point-slope form is `y=5(x+2)` .

(III) Horizontal line passes through (-2,6).
The equation of a horizontal line is in the form

`y=y_a`

where `y_a` represents the y-coordinate of the point.

Therefore, the equation of the horizontal line is `y=6` .

(IV) Vertical line that passes through (-2,6)
The equation of a vertical line is in the form

`x=x_a`

where x_a represents the x-coordinate of the point.

Thus, the equation of the vertical line is `x=-2` .

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