Question

consider the graph of 4x + 3y = -24 in item 12. which points represent ordered pairs that are solutions of the equation 4x + 3y = -24? select all that apply.
a the x-intercept of the graph
b the y-intercept of the graph
c the origin
d points that lie close to the line
e points that lie on the line

Explanation:

Step1: Recall solution definition

A solution to the linear equation \(4x + 3y=-24\) is an ordered pair \((x,y)\) that satisfies the equation. Geometrically, all solutions lie on the line represented by the equation.

Step2: Analyze each option

• Option A: The x - intercept is a specific point (when \(y = 0\), \(x=-6\)) on the line, but not all solutions are just the x - intercept.
• Option B: The y - intercept is a specific point (when \(x = 0\), \(y=-8\)) on the line, but not all solutions are just the y - intercept.
• Option C: The origin \((0,0)\): Substitute \(x = 0,y = 0\) into \(4x+3y\), we get \(0

eq - 24\), so the origin is not a solution.

• Option D: Points close to the line are not necessarily on the line, so they don't satisfy the equation.
• Option E: By the definition of a linear equation, all ordered pairs that are solutions lie on the line \(4x + 3y=-24\).

Answer:

E. points that lie on the line