$(2,5)$ and $(3,7)$ are two points on a line. a Find the slope of the line. b Write the equation of the line.
Explanation
The slope of the line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. In this case, the slope of the line passing through points $(2,5)$ and $(3,7)$ is $m = \frac{7 - 5}{3 - 2} = \frac{2}{1} = 2$. The equation of the line can be written in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. To find the equation of the line, we need to find the y-intercept $c$. We can use one of the points, say $(2,5)$, and substitute it into the equation to solve for $c$. This gives us $5 = 2(2) + c$, which simplifies to $c = 1$. Therefore, the equation of the line is $y = 2x + 1$.
⬆ Related Topic
📘 Syllabus
View STATE_KERALA Class 10 Syllabus →
📝 Practice Questions
Practice Previous Year Questions →
🤖 Practice with AI
Generate Practice Question Paper →