If the slope of line is `-(7)/(4)` and a point on the line is `(4, 7)`, what is the y-intercept of the line?

Answer

To find the y-intercept of the line given its slope and a point on the line, we can follow these steps:

### Step 1: Write the equation of the line in slope-intercept form
The slope-intercept form of a line is given by the equation:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept.

### Step 2: Substitute the slope into the equation
Given that the slope \( m \) is \( -\frac{7}{4} \), we can substitute this value into the equation:
\[ y = -\frac{7}{4}x + c \]

### Step 3: Substitute the point into the equation
We know that the line passes through the point \( (4, 7) \). Here, \( x = 4 \) and \( y = 7 \). We can substitute these values into the equation:
\[ 7 = -\frac{7}{4}(4) + c \]

### Step 4: Simplify the equation
Now, simplify the right-hand side:
\[ 7 = -\frac{7 \cdot 4}{4} + c \]
\[ 7 = -7 + c \]

### Step 5: Solve for \( c \)
To find \( c \), add 7 to both sides:
\[ 7 + 7 = c \]
\[ c = 14 \]

### Conclusion
The y-intercept \( c \) of the line is \( 14 \).

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