Question

question 1 of 5
one of the following is an equation of the linear relation shown in the standard (x,y) coordinate plane. which one is it?
a ( y = 3x )
b ( y = 7x + 3 )
c ( y = 3x - 7 )
d ( y = 3x + 7 )

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept (the value of \(y\) when \(x = 0\)).

Step2: Find the \(y\) - intercept

From the graph, when \(x = 0\), the line intersects the \(y\) - axis at \(y=7\). So the \(y\) - intercept \(b = 7\).

Step3: Analyze the slope

We can also check the slope. Let's take two points on the line. When \(x = 0\), \(y = 7\); when \(x = 1\), from the equation \(y=3x + 7\), \(y=3\times1 + 7=10\), which matches the graph's trend. The slope \(m\) of the line: looking at the options, the coefficient of \(x\) (the slope) should be 3 (since when \(x\) increases by 1, \(y\) increases by 3, as seen from \(x = 0,y = 7\) and \(x = 1,y = 10\) ( \(10 - 7=3\))).

Now let's check each option:

• Option A: \(y = 3x\) has a \(y\) - intercept of 0, but our graph has a \(y\) - intercept of 7. So A is incorrect.
• Option B: \(y=7x + 3\) has a slope of 7 and \(y\) - intercept of 3. The slope in our graph is 3 (not 7) and \(y\) - intercept is 7 (not 3). So B is incorrect.
• Option C: \(y = 3x-7\) has a \(y\) - intercept of - 7, but our graph has a \(y\) - intercept of 7. So C is incorrect.
• Option D: \(y=3x + 7\) has a slope of 3 and a \(y\) - intercept of 7, which matches our analysis.

Answer:

D. \(y = 3x + 7\)