Which of the following equations represents a line with a negative slope and a negative y-intercept?Select one:A. 3x+2y=−9B. x−y=−3C. y=4x−6D. y=−5x+8

Accepted Solution

Answer:A. [tex]3x+2y=-9[/tex]Step-by-step explanation:The standard form of a line in slope-intercept form is:[tex]y=mx+b[/tex]Where, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.Now, let us convert each option in this form.Option A:[tex]3x+2y=-9\\3x-3x+2y=-9-3x\\2y=-3x-9\\y=\frac{-3}{2}x-\frac{-9}{2}[/tex]Therefore, slope is [tex]-\frac{3}{2}[/tex] and y intercept is [tex]-\frac{9}{2}[/tex].Both slope and y intercept are negative. So, option A is correct.Option B:[tex]x-y=-3\\x-x-y=-3-x\\-y=-x-3\\y=x+3[/tex]Slope is 1 and y intercept is 3. Both are positive. So, option B is incorrect.Option C:[tex]y=4x-6[/tex]Slope is 4 and y intercept is -6. Both are not negative. So, option C is incorrect.Option D:[tex]y=-5x+8[/tex]Slope is -5 and y intercept is 8. Both are not negative. So, option D is incorrect.