This graph shows part of a straight line. Show that the gradient of the line is 2.5.
Understand the Problem
The question provides a graph of a straight line and asks to show that its gradient is 2.5. To do this, we need to choose two points on the line, calculate the change in y (rise) and the change in x (run) between these points, and then divide the rise by the run to find the gradient. We need to ensure our calculation results in 2.5 to complete the question.
Answer
The gradient of the line is $2.5$.
Answer for screen readers
The gradient of the line is $\frac{5}{2} = 2.5$.
Steps to Solve
- Identify two points on the line
From the graph, we can identify two points where the line intersects the grid precisely. Let's choose the points $(0, 0)$ and $(2, 5)$.
- Calculate the change in y (rise)
The change in $y$ is the difference in the $y$-coordinates of the two points.
$rise = y_2 - y_1 = 5 - 0 = 5$
- Calculate the change in x (run)
The change in $x$ is the difference in the $x$-coordinates of the two points.
$run = x_2 - x_1 = 2 - 0 = 2$
- Calculate the gradient
The gradient of the line is the rise divided by the run.
$gradient = \frac{rise}{run} = \frac{5}{2} = 2.5$
Therefore, the gradient of the line is 2.5.
The gradient of the line is $\frac{5}{2} = 2.5$.
More Information
The gradient of a line represents its steepness. A gradient of 2.5 means that for every 1 unit increase in $x$, the value of $y$ increases by 2.5 units.
Tips
A common mistake is misreading the coordinates of the points on the graph. Always double-check the $x$ and $y$ values of your chosen points to ensure accuracy. Another mistake is calculating $run/rise$ instead of $rise/run$, make sure to divide the change in $y$ by the change in $x$.
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