Answer:
Question:
The equation of a line has a y-intercept of 2 and a slope of 1/2. Which of the following is not true about the line?
Concept:
The general equation of a line in slope-intercept form is given below as
[tex]\begin{gathered} y=mx+c \\ m=slope=\frac{1}{2} \\ c=y-intercept=2 \end{gathered}[/tex]
By substituting the values, we will have that the equation of the line will be
[tex]\begin{gathered} y=mx+c \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]
Hence,
The equation of the line in slope intercept form is y=1/2x+2 (TRUE)
Step 2:
To figure out if the point (4,6) lies on the line, we will substitute the value of x=4 to get the value of y=6
[tex]\begin{gathered} y=\frac{1}{2}x+2,x=4 \\ y=\frac{1}{2}(4)+2 \\ y=2+2 \\ y=4 \end{gathered}[/tex]
Step 3:
To figure out if the point (20,12) lies on the line, we wil substitute the value of x=20 to get the value of y =12
[tex]\begin{gathered} y=\frac{1}{2}x+2,x=20 \\ y=\frac{1}{2}(20)+2 \\ y=10+2 \\ y=12 \end{gathered}[/tex]
Step 4:
The graph of the function is given below as
From the image above, we can see that the line will never pass through quadrant 4
Hence,
The final answer is
The point (4,6) is on the line (not true)
