Sure! Let's write the equation of the line that passes through the points [tex]\((-1, 2)\)[/tex] and [tex]\((6, 3)\)[/tex] in slope-intercept form [tex]\((y = mx + b)\)[/tex]. Follow these steps:
### Step 1: Identify the Coordinates
We are given the points [tex]\((-1, 2)\)[/tex] and [tex]\((6, 3)\)[/tex].
Let:
- [tex]\( (x_1, y_1) = (-1, 2) \)[/tex]
- [tex]\( (x_2, y_2) = (6, 3) \)[/tex]
### Step 2: Calculate the Slope (m)
The formula for the slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the given points into this formula:
[tex]\[ m = \frac{3 - 2}{6 - (-1)} \][/tex]
[tex]\[ m = \frac{1}{7} \][/tex]
[tex]\[ m \approx 0.14285714285714285 \][/tex]
### Step 3: Calculate the y-Intercept (b)
To find the y-intercept [tex]\( b \)[/tex], we use the slope-intercept form equation [tex]\( y = mx + b \)[/tex]. We can substitute one of the given points along with the slope into this equation to solve for [tex]\( b \)[/tex]. Let's use the point [tex]\((-1, 2)\)[/tex]:
[tex]\[ 2 = (0.14285714285714285) \cdot (-1) + b \][/tex]
[tex]\[ 2 = -0.14285714285714285 + b \][/tex]
[tex]\[ b = 2 + 0.14285714285714285 \][/tex]
[tex]\[ b = 2.142857142857143 \][/tex]
### Step 4: Write the Equation of the Line
Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
[tex]\[ y = 0.14285714285714285x + 2.142857142857143 \][/tex]
### Conclusion
The equation of the line that passes through the points [tex]\((-1, 2)\)[/tex] and [tex]\((6, 3)\)[/tex] in slope-intercept form is:
[tex]\[ y = 0.14285714285714285x + 2.142857142857143 \][/tex]
