Subjects algebra

Line Equation 144B57

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1. **State the problem:** We need to find the equation of the blue line shown on the graph. 2. **Identify points on the line:** From the description, the line passes through points $(0,2)$ and approximately $(1,5)$. 3. **Recall the formula for a line:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$:** The slope is the change in $y$ divided by the change in $x$ between two points: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{1 - 0} = \frac{3}{1} = 3$$ 5. **Identify the y-intercept $b$:** The line crosses the y-axis at $(0,2)$, so $b = 2$. 6. **Write the equation:** Substitute $m=3$ and $b=2$ into the formula: $$y = 3x + 2$$ **Final answer:** The equation of the blue line is $$y = 3x + 2$$.