Step 1
To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y
Step 2
A)
[tex]\begin{gathered} y=10-2x \\ To\text{ find the x-intercept set y=0} \\ 0=10-2x \\ 2x=10 \\ \frac{2x}{2}=\frac{10}{2} \\ x=5 \\ \text{Hence, the x-intercept in coordinate form will be (5,}0) \end{gathered}[/tex][tex]\begin{gathered} To\text{ find the y-intercept set x=0} \\ y=10-2x \\ y=10-2(0) \\ y=10 \\ \text{Hence, the y-intercept in coordinate form = (0,10)} \end{gathered}[/tex]Step 3
B)
[tex]\begin{gathered} 4y+9x=18 \\ To\text{ find the x-intercept we set y=0} \\ 4(0)+9x=18 \\ 9x=18 \\ \frac{9x}{9}=\frac{18}{9} \\ x=2 \\ \text{The x-intercept in coordinate form = (2,0)} \\ To\text{ find the y-intercept we set x=0} \\ 4y+9(0)=18 \\ 4y=18 \\ \frac{4y}{4}=\frac{18}{4} \\ y=4.5 \\ \text{The y-intercept in coordnate form = (0},4.5) \end{gathered}[/tex]Step 4
C)
[tex]\begin{gathered} 6x-2y=44 \\ To\text{ find the x-intercept we set y=0} \\ 6x-2(0)=44 \\ 6x=44 \\ \frac{6x}{6}=\frac{44}{6} \\ x=\frac{22}{3} \\ \text{The x-intercept in coordinate form = (}\frac{22}{3},0) \\ To\text{ find the x-intercept we set y=0} \\ 6(0)-2y=44 \\ -2y=44 \\ -\frac{2y}{-2}=\frac{44}{-2} \\ y=-22 \\ T\text{he y-intercept in coordinate form =}(0,-22) \end{gathered}[/tex]Step 5
D)
[tex]\begin{gathered} 2x=4+12y \\ To\text{ find the x-intercept we set y=0} \\ 2x=4+12(0) \\ 2x=4 \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \\ \text{The x-intercept in coordinate form =(2,0}) \\ To\text{ find the y-intercept we set x=0} \\ 2(0)=4+12y \\ 0=4+12y \\ 12y=-4 \\ \frac{12y}{12}=-\frac{4}{12} \\ y=-\frac{1}{3} \\ \text{The y-intercept in coordinate form= (0,-}\frac{1}{3}) \end{gathered}[/tex]Therefore, we can summarize the x and y-intercepts of the individual functions on a table thus;
