Graph the Linear Function: Y = 5X

Linear Function Graphing with Steep Slopes

Y is a function of X that matches 5 times X .

Which graph represents the function described above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Draw the function graph
00:03 Function equation according to the given data
00:06 Substitute values in X and find the corresponding Y values according to the given data
00:12 Plot each point in our coordinate system
00:18 Draw the appropriate graph
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Y is a function of X that matches 5 times X .

Which graph represents the function described above?

2

Step-by-step solution

To find the correct graph, follow these steps:

  • Step 1: Identify the equation Y=5X Y = 5X as a linear function with a slope of 5 and a y-intercept of 0.
  • Step 2: Locate the graph that depicts a line passing through the origin (0,0) with a steep rise indicating a slope of 5.
  • Step 3: Examine the given choices to see which one fits this description.

After examining the choices, the appropriate graph shows a line passing through the origin with the correct slope of 5. The correct representation of the function Y=5X Y = 5X is:

–17–17–17–16–16–16–15–15–15–14–14–14–13–13–13–12–12–12–11–11–11–10–10–10–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010–15–15–15–10–10–10–5–5–5

3

Final Answer

–17–17–17–16–16–16–15–15–15–14–14–14–13–13–13–12–12–12–11–11–11–10–10–10–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010–15–15–15–10–10–10–5–5–5

Key Points to Remember

Essential concepts to master this topic
  • Slope-Intercept Form: Y=5X Y = 5X has slope 5 and y-intercept 0
  • Technique: Line passes through origin (0,0) and point (1,5)
  • Check: When X = 1, Y = 5(1) = 5; graph shows point at (1,5) ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope magnitude with direction
    Don't think slope 5 makes a gradual line = wrong graph selection! A slope of 5 means rise 5 units for every 1 unit right, creating a very steep upward line. Always remember larger slope numbers mean steeper lines.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

FAQ

Everything you need to know about this question

How do I know which graph has the right slope?

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Look for a line that rises 5 units up for every 1 unit right. The slope of 5 creates a very steep line going upward from left to right.

Why does the line pass through the origin?

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Because there's no constant term in Y=5X Y = 5X , the y-intercept is 0. This means when X = 0, Y = 0, so the line passes through point (0,0).

What if I can't tell which line is steeper?

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Pick a point like X = 1 and calculate: Y=5(1)=5 Y = 5(1) = 5 . The correct graph should show the line passing through (1,5). Look for this specific point!

How is this different from Y = X?

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Y=X Y = X has slope 1 (rises 1 unit per 1 unit right), while Y=5X Y = 5X has slope 5 (rises 5 units per 1 unit right). The line with slope 5 is much steeper!

Can the slope be negative?

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Yes! If the equation was Y=−5X Y = -5X , the line would be equally steep but slope downward from left to right instead of upward.

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