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).
(I) Slope is -8 and y-intercept is 3.
The slope-intercept form of a line is
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
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:
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
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
where x_a represents the x-coordinate of the point.
Thus, the equation of the vertical line is `x=-2` .