MATH SOLVE

3 months ago

Q:
# Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –y equals negative StartFraction one-third EndFraction x plus 9.x + 9 y = –y equals negative StartFraction one-third EndFraction x plus 5.x + 5 y = –3x – 11y y = –3x + 25

Accepted Solution

A:

Answer:[tex]y=-\frac{1}{3} x+5[/tex]Step-by-step explanation:Notice that the answers they give you to choose from are all lines in slope y-intercept form, it would be very simple to just find the answer finding yourself the slope and y-intercept of the line in question. Since they give you two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] for the line, use them to find the slope of the line that goes through them, with the formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1} =\frac{7-6}{-6-(-3)} =\frac{1}{-3} =-\frac{1}{3}[/tex]Therefore, the slope of the line must be [tex]-\frac{1}{3}[/tex]Now, find the y-intercept (b) using the general form of a line with the given slope:[tex]y=-\frac{1}{3}x +b[/tex]Use one of the given coordinate points to request that the line passes through it. For example, through the point (-3,6) (when x = -3, y must be 6):[tex]y=-\frac{1}{3} x+b\\6=-\frac{1}{3}(-3)+b\\6=1+b\\b=6-1=5[/tex]then the y-intercept must be 5. Therefore our line is : [tex]y=-\frac{1}{3}x +5[/tex] which appears listed as your second choice.