Question

(0,1) and (1,-4) write the equation of the line in slope intercept form

Answer 1

To find the equation of a line in slope-intercept form (\(y = mx + b\)), given two points \((x_1, y_1)\) and \((x_2, y_2)\), we need to follow these steps:

1. Calculate the slope (\(m\)) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

2. Use the slope (\(m\)) and one of the points to solve for the y-intercept (\(b\)).

Given points \((0, 1)\) and \((1, -4)\):

**Step 1: Calculate the slope (\(m\))**

Substitute the given points into the slope formula:
\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

**Step 2: Use the slope and one of the points to find the y-intercept (\(b\))**

We can use the point \((0, 1)\) because it is straightforward when the x-coordinate is zero, which means this point is the y-intercept itself.

Since the point (0, 1) is a y-intercept, we have:
\[
b = 1
\]

**Step 3: Write the equation in slope-intercept form (\(y = mx + b\))**

Now that we have \(m = -5\) and \(b = 1\), we can write the equation of the line:
\[
y = -5x + 1
\]

Hence, the equation of the line passing through the points \((0, 1)\) and \((1, -4)\) in slope-intercept form is:
\[
y = -5x + 1
\]