To write the equation of a line in slope-intercept form [tex]\( y = mx + b \)[/tex], given two points, let's carefully go through the method step-by-step.
Step 1: Find the Slope
Given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], the first step is to determine the slope [tex]\( m \)[/tex] using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Step 2: Use the Slope to Find the y-Intercept
Once we have the slope [tex]\( m \)[/tex], we need to find the y-intercept [tex]\( b \)[/tex]. To do this, we substitute the slope [tex]\( m \)[/tex] and one of the given points into the equation [tex]\( y = mx + b \)[/tex]. We can use either of the given points; let's use [tex]\((x_1, y_1)\)[/tex] for this example:
[tex]\[ y_1 = m x_1 + b \][/tex]
Solve for [tex]\( b \)[/tex] by rearranging the equation:
[tex]\[ b = y_1 - m x_1 \][/tex]
Step 3: Write the Equation
Now that we have both the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[ y = m x + b \][/tex]
Among the given choices, the correct method is:
1. Find the slope using the formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex], and then substitute one point and the slope into the equation [tex]\( y = mx + b \)[/tex] to find the y-intercept.
So the correct choice is:
1
