Math  /  Algebra

QuestionWhen discussing the key features of a linear graph, which of the following statements is true? (1 point) The points will make a straight line. The initial value is always zero. The rate of change can vary along the graph. The points always have positive values.

Studdy Solution

STEP 1

What is this asking? Which statement is true about linear graphs? Watch out! Don't get tricked by statements that might *sometimes* be true but aren't *always* true for *every* linear graph!

STEP 2

1. Straight Line Check
2. Initial Value Check
3. Rate of Change Check
4. Positive Values Check

STEP 3

A linear graph, by definition, is the graph of a linear function.
What's a linear function?
It's a function whose graph is a straight line!
So, the statement "The points will make a straight line" is **absolutely true**!

STEP 4

The **initial value** is the yy-value when x=0x = 0.
Think about the line y=x+1y = x + 1.
When x=0x = 0, y=1y = 1.
The initial value is 1\mathbf{1}, not zero!
So, the statement "The initial value is always zero" is **false**!

STEP 5

The **rate of change**, also known as the **slope**, tells us how much the yy-value changes for every unit change in xx.
For a straight line, this rate of change is **constant**!
Think about it: if the slope kept changing, the line would be curvy, not straight!
So, the statement "The rate of change can vary along the graph" is **false**!

STEP 6

Think about the line y=xy = -x.
When x=1x = 1, y=1y = -1.
A perfectly valid point on a linear graph, but yy is negative!
So, the statement "The points always have positive values" is **false**!

STEP 7

The correct statement is: The points will make a straight line.

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