Question

a line passes through (0,5) and (2,9). what is the equation of the line in slope - intercept form?
○ $y = 2x + 5$
○ $y = 5x + 2$
○ $y = 4x + 5$
○ $y = 2x + 9$

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(0,5)\) and \((x_2, y_2)=(2,9)\). So \( m=\frac{9 - 5}{2 - 0}=\frac{4}{2}=2\).

Step2: Find the y - intercept

The slope - intercept form of a line is \( y = mx + b\), where \( b \) is the y - intercept. The line passes through \((0,5)\), when \( x = 0\), \( y=b\). So \( b = 5\).

Step3: Write the equation

Substitute \( m = 2\) and \( b = 5\) into \( y=mx + b\), we get \( y=2x + 5\). We can also check by plugging \( x = 2\) into \( y = 2x+5\), \( y=2\times2 + 5=4 + 5 = 9\), which matches the point \((2,9)\).

Answer:

A. \( y = 2x+5 \)