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 L drawn on a grid. The equation should be in the form y = mx + c, where 'm' is the slope and 'c' is the y-intercept of the line.
Answer
$ y = \frac{3}{2}x + 2 $
Answer for screen readers
$ y = \frac{3}{2}x + 2 $
Steps to Solve
- Determine two points on the line
From the graph, we can identify two points where the line L intersects the grid clearly. Let's take $(0, 2)$ and $(2, 5)$.
- 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 the points $(0, 2)$ and $(2, 5)$, we have: $$ m = \frac{5 - 2}{2 - 0} = \frac{3}{2} $$
- Determine the y-intercept (c)
The y-intercept is the point where the line crosses the y-axis (i.e., when $x = 0$). From the graph, we can see that the line intersects the y-axis at $y = 2$. Therefore, $c = 2$. Alternatively, we can substitute one of the points we know (e.g. $(0, 2)$) into the equation $y = mx + c$, along with the $m$ we just calculated, and solve for $c$.
$2 = \frac{3}{2} * 0 + c$ $c = 2$
- Write the equation of the line
Now that we have the slope $m = \frac{3}{2}$ and the y-intercept $c = 2$, we can write the equation of the line in the form $y = mx + c$: $$ y = \frac{3}{2}x + 2 $$
$ y = \frac{3}{2}x + 2 $
More Information
The equation represents a straight line where for every 2 units you move to the right on the x-axis, the line goes up 3 units on the y-axis, and it crosses the y-axis at the point (0, 2).
Tips
A common mistake here includes misreading the graph while calculating the slope and y-intercept. Ensure you accurately read points from the graph and substitute them into the equation. Also, mixing up the formula for slope, calculating it as $m = \frac{x_2 - x_1}{y_2 - y_1}$ will lead to an incorrect answer.
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