MATH SOLVE

9 months ago

Q:
# Which of the following shows the graph of a line with a slope of 6/5 and a y intercept of -3?

Accepted Solution

A:

Answer:The correct option is 1.Step-by-step explanation:It is given that the slope of the line is 6/5 and y intercept is -3. It means the line must be passes through the point (0,-3).The slope intercept form of a line is[tex]y=mx+b[/tex]where, m is slope and b is y-intercept.Substitute m=6/5 and b=-3 in the above equation to find the equation of line.[tex]y=\frac{6}{5}x+(-3)[/tex]So, the equation of line is [tex]y=\frac{6}{5}x+(-3)[/tex].Substitute y=0 in the above equation to find the x-intercept of the line.[tex]0=\frac{6}{5}x-3[/tex]Add 3 on both the sides.[tex]0+3=\frac{6}{5}x-3+3[/tex][tex]3=\frac{6}{5}x[/tex]Multiply both sides by 5.[tex]15=6x[/tex]Divide both sides by 6.[tex]\frac{15}{6}=x[/tex][tex]2.5=x[/tex]The x-intercept of the line is 2.5. It means the line must be passes through the point (2.5,0).Since only in graph 1, the line passes through the points (0,-3) and (2.5,0), therefore the graph 1 represents the required line and option 1 is correct.