Find the slope of the lines joining each of the following pair of points. (4,-1) and (4,3)
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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:
This formula can also be written as
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.
<h3>Note</h3>In the attached graph, the first graph is represented by the red line while the graph of the new function is in blue.
