write the equation of the line that passes through the points (0,5) & (-3,17) make the answer clear and make sense

1 answer

To find the equation of the line that passes through the points (0, 5) and (-3, 17), we will use the slope-intercept form of a linear equation, which is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

Step 1: Calculate the slope (m)

The slope \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let’s denote the points as follows:

  • Point 1: \( (x_1, y_1) = (0, 5) \)
  • Point 2: \( (x_2, y_2) = (-3, 17) \)

Substituting the coordinates into the slope formula:

\[ m = \frac{17 - 5}{-3 - 0} = \frac{12}{-3} = -4 \]

Step 2: Use the slope and one point to find the y-intercept (b)

We know that the line passes through (0, 5). Since this point is the y-intercept (where \( x = 0 \)), we can determine the y-intercept \( b \) directly:

\[ b = 5 \]

Step 3: Write the equation of the line

Now that we have the slope \( m = -4 \) and the y-intercept \( b = 5 \), we can write the equation of the line:

\[ y = -4x + 5 \]

Conclusion

The equation of the line that passes through the points (0, 5) and (-3, 17) is

\[ \boxed{y = -4x + 5} \]