Find the equation for the straight line L. Give your answer in the form y = mx + c
Understand the Problem
The question asks to find the equation of a straight line, labelled L, given its representation on a coordinate grid. The final answer must be given in the form y = mx + c, where 'm' represents the slope of the line, and 'c' represents the y-intercept.
Answer
$y = 2x + 2$
Answer for screen readers
$y = 2x + 2$
Steps to Solve
- Identify two points on the line
From the graph, we can identify two points where the line L intersects the grid clearly. Let's choose the points (0,2) and (2,6).
- Calculate the slope (m)
The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Using our chosen points (0,2) and (2,6):
$m = \frac{6 - 2}{2 - 0} = \frac{4}{2} = 2$
- Determine the y-intercept (c)
The y-intercept is the point where the line crosses the y-axis. From the graph (or our chosen point (0,2)), we can see that the line crosses the y-axis at y = 2. Thus, $c = 2$.
- Write the equation in the form y = mx + c
Now that we have the slope $m = 2$ and the y-intercept $c = 2$, we can write the equation of the line:
$y = 2x + 2$
$y = 2x + 2$
More Information
The equation $y = 2x + 2$ represents a straight line with a slope of 2 and intersects the y-axis at the point (0, 2).
Tips
A common mistake is misreading the coordinates of the points on the line. Always double-check the x and y values carefully. Another mistake is incorrectly calculating the slope, so ensure the formula is applied correctly, with consistent subtraction order for both the numerator and denominator. Finally, some may mix up the slope and y-intercept in the equation.
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