Question

1. consider the graph in item 12. which points represent ordered pairs that are solutions of the equation 4x + 8y = 16? select all that apply. a. the origin b. the x-intercept of the graph c. the y-intercept of the graph d. points that lie on the line e. points that lie close to the line

Explanation:

Step1: Check Option A (Origin)

Substitute \(x = 0\), \(y = 0\) into \(4x + 8y = 16\).
Left - hand side (LHS) \(= 4(0)+8(0)=0\), Right - hand side (RHS) \( = 16\).
Since \(0
eq16\), the origin is not a solution.

Step2: Check Option B (x - intercept)

For x - intercept, \(y = 0\). Substitute \(y = 0\) into \(4x+8y = 16\):
\(4x+8(0)=16\Rightarrow4x = 16\Rightarrow x = 4\).
So the x - intercept is \((4,0)\). Substitute \(x = 4\), \(y = 0\) into \(4x + 8y\):
\(4(4)+8(0)=16 + 0=16\), which equals RHS. So \((4,0)\) is a solution.

Step3: Check Option C (y - intercept)

For y - intercept, \(x = 0\). Substitute \(x = 0\) into \(4x + 8y=16\):
\(4(0)+8y = 16\Rightarrow8y=16\Rightarrow y = 2\).
So the y - intercept is \((0,2)\). Substitute \(x = 0\), \(y = 2\) into \(4x + 8y\):
\(4(0)+8(2)=0 + 16=16\), which equals RHS. So \((0,2)\) is a solution.

Step4: Check Option D (Points on the line)

By definition, the points on the graph of the equation \(4x + 8y=16\) are the ordered pairs \((x,y)\) that satisfy the equation (i.e., make \(4x + 8y = 16\) true). So all points on the line are solutions.

Step5: Check Option E (Points close to the line)

Points close to the line do not necessarily satisfy the equation \(4x + 8y = 16\). For example, take a point \((1,1)\) (close to the line). Substitute into \(4x + 8y\): \(4(1)+8(1)=12
eq16\). So points close to the line are not solutions.

Answer:

B. the x - intercept of the graph, C. the y - intercept of the graph, D. points that lie on the line