The given equation is
[tex]y=-2x+7[/tex]We have to find the axis interceptions to graph this function.
For x = 0, we have
[tex]y=-2(0)+7=0+7=7[/tex]The y-interception is (0,7).
For y = 0, we have
[tex]\begin{gathered} 0=-2x+7 \\ 2x=7 \\ x=\frac{7}{2} \end{gathered}[/tex]The x-interception is (7/2, 0).
Now, we graph.
Where h is the hypothenuse.
To find the hypothenuse of the right triangle formed, we use the distance formula and both points.
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Replacing the coordinates, we have
[tex]\begin{gathered} d=\sqrt[]{(0-7)^2+(3.5-0)^2}=\sqrt[]{(-7)^2+(3.5)^2} \\ d=\sqrt[]{49+12.25}=\sqrt[]{61.25}\approx7.83 \end{gathered}[/tex]Therefore, the hypotenuse is 7.83 units long, approximately.
At last, the area of the triangle is found with the formula
[tex]A=\frac{1}{2}b\cdot h[/tex]Where b is the base and h is the height of the triangle. b = 3.5, h = 7.
Replacing these values, we have
[tex]A=\frac{1}{2}(3.5)\cdot(7)=\frac{24.5}{2}=12.25u^2[/tex]Therefore, the area of the triangle is 12.25 square units.
