Question

write an equation of the line that passes through (3, 1) and (0, 10)
y = \square

Explanation:

Step1: Find the slope (m)

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(3, 1)\) and \((x_2, y_2)=(0, 10)\). So, \(m=\frac{10 - 1}{0 - 3}=\frac{9}{-3}=-3\).

Step2: Use the y - intercept form

The y - intercept form of a line is \(y = mx + b\), where \(b\) is the y - intercept. We know that the line passes through \((0, 10)\), so when \(x = 0\), \(y = 10\). This means \(b = 10\). We already found that \(m=-3\). Substituting \(m=-3\) and \(b = 10\) into the equation \(y=mx + b\), we get \(y=-3x + 10\).

Answer:

\(y=-3x + 10\)