To complete the table and find the x- and y-intercepts for the equation ( y = -2x + 3 ), follow these steps:
Table of Values
Choose values for ( x ) and calculate the corresponding ( y ) values.
Let ( x = 0 ):
[
y = -2(0) + 3 = 3
]
So, ( (0, 3) ).
Let ( x = 1 ):
[
y = -2(1) + 3 = 1
]
So, ( (1, 1) ).
Let ( x = 2 ):
[
y = -2(2) + 3 = -1
]
So, ( (2, -1) ).
Now the table can be filled in as:
[
\begin{array}{c|c}
x & y \
\hline
0 & 3 \
1 & 1 \
2 & -1 \
\end{array}
]
X-Intercept
To find the x-intercept, set ( y = 0 ) and solve for ( x ).
[
0 = -2x + 3 \
2x = 3 \
x = \frac{3}{2}
]
So, the x-intercept is ( \left(\frac{3}{2}, 0\right) ).
Y-Intercept
To find the y-intercept, set ( x = 0 ) which we've already calculated:
[
y = 3
]
So, the y-intercept is ( (0, 3) ).
These points are useful for graphing the linear equation.
