MATH SOLVE

4 months ago

Q:
# Instructions:Select the correct answer from each drop-down menu.The slope of the line passing through the points (7, 5) and (21, 15) is _____.A.) 5/7 B.) 7/5 C.) 5 D.) 7 Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point _____.A.) (3, 5) B.) (3, 7) C.) (21, 5) D.) (21, 7)

Accepted Solution

A:

Answer:Part A: Option APart B: Option CStep-by-step explanation:Given two points (7, 5) and (21, 15)we have to find the slope of the line passing through above two points.The slope of line can be calculated as[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{15-5}{21-7}=\frac{10}{14}=\frac{5}{7}[/tex]Option A is correct. Part B: Also given another line with a slope that is one-third that of the slope of above and passes through the origin and the point we have to find the point.[tex]slope=\frac{1}{3}\times \frac{5}{7}=\frac{5}{21}[/tex]The equation of line becomes [tex]y-y'=m(x-x')[/tex][tex]y-0=\frac{5}{21}(x-0)[/tex][tex]21y=5x[/tex]The point which satisfies the above equation passes through the line.[tex](3,5):21(5)=5(3)[/tex] Not satisfied[tex](3,7):21(7)=5(3)[/tex] Not satisfied[tex](21,5):21(5)=5(21)[/tex] Satisfied [tex](21,7):21(7)=2(21)[/tex] Not satisfied Hence, the line passes through the point (21, 5)Option C is correct.