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Question

Changing Slope and y-intercept Quick Check
3 of 53 of 5 Items
Question
Predict how the graph of the lines y=x−4
and y=7x+3
are different from each other.(1 point)
Responses

The graph of y=7x+3
is steeper and more vertical than y=x−4
.
The graph of y is equal to 7 x plus 3 is steeper and more vertical than y is equal to x minus 4.

The graph of y=x−4
is steeper and more vertical than y=7x+3
.
The graph of y is equal to x minus 4 is steeper and more vertical than y is equal to 7 x plus 3.

The graphs have the same slope but different y-intercepts.
The graphs have the same slope but different y -intercepts.

The graphs of y=7x+3
has a positive slope, and the graph of y=x−4
has a negative slope.

Answer 1

To predict how the graphs of the lines \(y = x - 4\) and \(y = 7x + 3\) are different from each other, we need to analyze their slopes.

1. The equation \(y = x - 4\) has a slope of 1 (the coefficient of \(x\)), and a y-intercept of -4.
2. The equation \(y = 7x + 3\) has a slope of 7 and a y-intercept of 3.

Given this information, we can conclude that the graph of \(y = 7x + 3\) is steeper than that of \(y = x - 4\) because it has a larger slope (7 vs. 1).

So the correct response is:

The graph of \(y = 7x + 3\) is steeper and more vertical than \(y = x - 4\).