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Due on May 26, 2024 11:59 PM. It will be turned in automatically after the due date passes.
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Find the equation of the line passing through the points (0, 4) and (-3, -11).
y = 0
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Ex 1: Find the Equation of a Line in ...

Verified Answer :

GinnyAnswer

To find the equation of a line passing through two points, you need to follow several steps which involve calculating the slope of the line and then using the slope to find the y-intercept. We will work through these steps using the given points \(\((0, 4)\)\) and \(\((-3, -11)\)\).

### Step 1: Calculate the slope (m) of the line
The formula for the slope \(\(m\)\) between two points \(\((x_1, y_1)\)\) and \(\((x_2, y_2)\)\) is given by:

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

Substitute the given points into the formula:
\(\[ (x_1, y_1) = (0, 4) \]\)
\(\[ (x_2, y_2) = (-3, -11) \]\)

Now, plug these values into the slope formula:
\(\[ m = \frac{-11 - 4}{-3 - 0} \]\)
\(\[ m = \frac{-15}{-3} \]\)
\(\[ m = 5 \]\)

### Step 2: Use the point-slope form to find the equation
The point-slope form of the equation of a line is:
\(\[ y - y_1 = m(x - x_1) \]\)

Using point \(\((x_1, y_1) = (0, 4)\)\) and the slope \(\(m = 5\)\), we substitute these values into the point-slope form:
\(\[ y - 4 = 5(x - 0) \]\)
Simplifying this equation:
\(\[ y - 4 = 5x \]\)

### Step 3: Solve for \(\( y \)\) to get the slope-intercept form
To express the equation in the slope-intercept form \(\( y = mx + b \)\):
\(\[ y - 4 = 5x \]\)
Add 4 to both sides to isolate \(\( y \)\):
\(\[ y = 5x + 4 \]\)

### Conclusion
Therefore, the equation of the line passing through the points \(\((0, 4)\)\) and \(\((-3, -11)\)\) is:

\(\[ y = 5x + 4 \]\)

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