Fing y if the slope of the line containing the point (-1,3) and (4,y) is 0.75

Options

A. 0.75
B. 1
C. 6.75
D. 8

Explanation

To find the value of \( y \) such that the slope of the line containing the points \((-1, 3)\) and \((4, y)\) is \(0.75\), we can follow these steps:

### Step 1: Understand the slope formula
The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Assign the points
Let \((x_1, y_1) = (-1, 3)\) and \((x_2, y_2) = (4, y)\). Here, \( x_1 = -1 \), \( y_1 = 3 \), \( x_2 = 4 \), and \( y_2 = y \).

### Step 3: Substitute into the slope formula
Substituting the values into the slope formula, we have:
\[ 0.75 = \frac{y - 3}{4 - (-1)} \]

### Step 4: Simplify the denominator
Calculate the denominator:
\[ 4 - (-1) = 4 + 1 = 5 \]
So the equation becomes:
\[ 0.75 = \frac{y - 3}{5} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 0.75 \times 5 = y - 3 \]
Calculating \(0.75 \times 5\):
\[ 3.75 = y - 3 \]

### Step 6: Solve for \( y \)
Add \(3\) to both sides to isolate \(y\):
\[ y = 3.75 + 3 \]
\[ y = 6.75 \]

### Final Answer
Thus, the value of \( y \) is:
\[ \boxed{6.75} \]

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