Drag and drop the tiles with the coordinate points, so they match up with an equation that they satisfy.

Understand the Problem

The question is asking to match coordinate points with corresponding linear equations. Each point should satisfy one of the given equations, so we need to determine which points belong to which equation based on linear function principles.

Answer

Matches are: - $(0, 5)$ with $y = 13x + 5$ - $(0, 0)$ with $y = -3x$ - $(8, -2)$ with $y = x - 10$ - $(-2, -21)$ with $y = 13x + 5$ - $(-5, -15)$ with $y = x - 10$ - $(-3, 9)$ with $y = -3x$

Steps to Solve

Identify the equations and their forms

We have three linear equations to work with:
- $y = 13x + 5$
- $y = -3x$
- $y = x - 10$
Evaluate the first point (0, 5)

Substitute $x = 0$ into the equations:
- For $y = 13x + 5$: $$y = 13(0) + 5 = 5$$
- For $y = -3x$: $$y = -3(0) = 0$$
- For $y = x - 10$: $$y = 0 - 10 = -10$$
The point $(0, 5)$ satisfies the equation $y = 13x + 5$.
Evaluate the next point (0, 0)

Substitute $x = 0$:
- For $y = 13x + 5$: $$y = 13(0) + 5 = 5$$
- For $y = -3x$: $$y = -3(0) = 0$$
- For $y = x - 10$: $$y = 0 - 10 = -10$$
The point $(0, 0)$ satisfies the equation $y = -3x$.
Evaluate point (8, -2)

Substitute $x = 8$:
- For $y = 13x + 5$: $$y = 13(8) + 5 = 104 + 5 = 109$$
- For $y = -3x$: $$y = -3(8) = -24$$
- For $y = x - 10$: $$y = 8 - 10 = -2$$
The point $(8, -2)$ satisfies the equation $y = x - 10$.
Evaluate point (-2, -21)

Substitute $x = -2$:
- For $y = 13x + 5$: $$y = 13(-2) + 5 = -26 + 5 = -21$$
- For $y = -3x$: $$y = -3(-2) = 6$$
- For $y = x - 10$: $$y = -2 - 10 = -12$$
The point $(-2, -21)$ satisfies the equation $y = 13x + 5$.
Evaluate point (-5, -15)

Substitute $x = -5$:
- For $y = 13x + 5$: $$y = 13(-5) + 5 = -65 + 5 = -60$$
- For $y = -3x$: $$y = -3(-5) = 15$$
- For $y = x - 10$: $$y = -5 - 10 = -15$$
The point $(-5, -15)$ satisfies the equation $y = x - 10$.
Evaluate point (-3, 9)

Substitute $x = -3$:
- For $y = 13x + 5$: $$y = 13(-3) + 5 = -39 + 5 = -34$$
- For $y = -3x$: $$y = -3(-3) = 9$$
- For $y = x - 10$: $$y = -3 - 10 = -13$$
The point $(-3, 9)$ satisfies the equation $y = -3x$.
Evaluate point (-2, -21) again for cross-check

(Already done in step 5)
Finalize the matches
- $(0, 5)$ matches with $y = 13x + 5$
- $(0, 0)$ matches with $y = -3x$
- $(8, -2)$ matches with $y = x - 10$
- $(-2, -21)$ matches with $y = 13x + 5$
- $(-5, -15)$ matches with $y = x - 10$
- $(-3, 9)$ matches with $y = -3x$

$(0, 5)$ matches with $y = 13x + 5$
$(0, 0)$ matches with $y = -3x$
$(8, -2)$ matches with $y = x - 10$
$(-2, -21)$ matches with $y = 13x + 5$
$(-5, -15)$ matches with $y = x - 10$
$(-3, 9)$ matches with $y = -3x$

More Information

Linear equations can represent a variety of lines in a coordinate system. Each equation can be verified by substituting the values of the point into the equation.

Tips

Forgetting to substitute the values into all equations for each point can lead to incorrect matching.
Miscalculating the value of $y$ when substituting can cause errors in identifying the correct equation. Double-check your calculations.

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