Question

*2. the graph of a line in the xy-plane passes through the point with coordinates (6,2) and crosses the x-axis at the point with coordinates (10,0). the line crosses the y-axis at the point with coordinates (0,b). what is the value of b?

Explanation:

Step1: Find the slope of the line

The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((10,0)\) and \((6,2)\), we have \( m=\frac{2 - 0}{6 - 10}=\frac{2}{-4}=-\frac{1}{2} \).

Step2: Use point - slope form to find the equation of the line

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((10,0)\) and \( m =-\frac{1}{2} \), we get \( y-0=-\frac{1}{2}(x - 10) \), which simplifies to \( y=-\frac{1}{2}x + 5 \).

Step3: Find the y - intercept (value of \( b \))

The equation of the line in slope - intercept form is \( y=mx + b \), where \( b \) is the y - intercept. From the equation \( y=-\frac{1}{2}x + 5 \), when \( x = 0 \), \( y=b = 5 \).

Answer:

\( 5 \)