Question

which ordered pairs are solutions to the equation? select all that apply.
(4, 5) (2, -6) (5, -4)
(-6, 0) (-2, 2) (2, 0)

Explanation:

Step1: Find the equation of the line

The line passes through \((0, 3)\) (y - intercept) and \((-6, 0)\) (x - intercept). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 0}{0-(-6)}=\frac{3}{6}=\frac{1}{2}\). Using the slope - intercept form \(y = mx + b\), where \(m=\frac{1}{2}\) and \(b = 3\), the equation is \(y=\frac{1}{2}x + 3\).

Step2: Check each ordered pair

• For \((4,5)\): Substitute \(x = 4\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(4)+3=2 + 3=5\). So \((4,5)\) is a solution.
• For \((2,-6)\): Substitute \(x = 2\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(2)+3=1 + 3 = 4

eq-6\). So \((2,-6)\) is not a solution.

• For \((5,-4)\): Substitute \(x = 5\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(5)+3=\frac{5}{2}+3=\frac{5 + 6}{2}=\frac{11}{2}=5.5

eq-4\). So \((5,-4)\) is not a solution.

• For \((-6,0)\): Substitute \(x=-6\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(-6)+3=-3 + 3=0\). So \((-6,0)\) is a solution.
• For \((-2,2)\): Substitute \(x=-2\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(-2)+3=-1 + 3=2\). So \((-2,2)\) is a solution.
• For \((2,0)\): Substitute \(x = 2\) into \(y=\frac{1}{2}x + 3\), we get \(y=\frac{1}{2}(2)+3=1 + 3=4

eq0\). So \((2,0)\) is not a solution.

Answer:

\((4,5)\), \((-6,0)\), \((-2,2)\)