Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote

If y = 3x + 1 is changed to y = 4x + 1, how would the graph of the new function compare with

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Answer:

The graph of the new function would be steeper than the first one.

Step-by-step explanation:

<h3>Slope-intercept form</h3>

y= mx +c, where m is the gradient and c is the y-intercept. Note that in this form, the y term is the only term on the left-hand side of the equation and its coefficient is 1.

<h3>Identifying gradients</h3>

Since the two equations are in the slope-intercept form, we can easily identify their gradients from the coefficient of x.

The gradient of the first graph is 3, while that of the new function is 4.

<h3>Implications of a greater gradient</h3>

The gradient of a graph is how steep it is, or the change of y with respect to x. Also when we are given a linear graph without its equation, we can find its gradient using the formula:

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

This formula can also be written as

$\boxed{ slope = \frac{rise }{run} }$

These formulas imply that the gradient is the looking at how much the y- coordinate changes with respect to x. The term 'gradient' and 'slope' have the same meaning and is used interchangeably here.

Given that the new function has a greater slope, it has a greater change in y with respect to x than the first graph. Thus, we see a steeper graph when y= 3x +1 is changed to y= 4x +1.

<h3>y- intercepts</h3>

The y-intercept does not change in this case and both graphs intercept the y-axis at y= 1.

In the attached graph, the first graph is represented by the red line while the graph of the new function is in blue.