Question

The line y=mx+c passes through the points (2,5) and (-1,-5).find m and c

Answer 1

To find the slope \( m \) and the y-intercept \( c \) of the line \( y = mx + c \) that passes through the points \( (2, 5) \) and \( (-1, -5) \), we can follow these steps:

1. **Calculate the slope \( m \)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) = (2, 5) \) and \( (x_2, y_2) = (-1, -5) \).

Plugging in the values:
\[
m = \frac{-5 - 5}{-1 - 2} = \frac{-10}{-3} = \frac{10}{3}
\]

2. **Use the point-slope form to find \( c \)**.
We use one of the points to find \( c \). Let's use the point \( (2, 5) \):
\[
y = mx + c
\]
Substituting \( x = 2 \), \( y = 5 \), and \( m = \frac{10}{3} \):
\[
5 = \frac{10}{3} \cdot 2 + c
\]
\[
5 = \frac{20}{3} + c
\]
To solve for \( c \), subtract \( \frac{20}{3} \) from both sides:
\[
c = 5 - \frac{20}{3}
\]
We need a common denominator to subtract:
\[
5 = \frac{15}{3}
\]
Thus:
\[
c = \frac{15}{3} - \frac{20}{3} = \frac{15 - 20}{3} = \frac{-5}{3}
\]

3. **Summary of results**:
The slope \( m \) is \( \frac{10}{3} \) and the intercept \( c \) is \( -\frac{5}{3} \).

So, the equation of the line is:
\[
y = \frac{10}{3}x - \frac{5}{3}
\]