Questions: A line passes through the point (-1,4) and has a slope of 7. Write an equation in slope-intercept form for this line.

A line passes through the point (-1,4) and has a slope of 7. Write an equation in slope-intercept form for this line.
Transcript text: A line passes through the point $(-1,4)$ and has a slope of 7 . Write an equation in slope-intercept form for this line.
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Solution

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Solution Steps

To write the equation of a line in slope-intercept form (y = mx + b) given a point and the slope, we can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \). Here, \( m \) is the slope and \( (x_1, y_1) \) is the given point. We can then solve for \( y \) to convert it to slope-intercept form.

Solution Approach
  1. Start with the point-slope form: \( y - y_1 = m(x - x_1) \).
  2. Substitute the given point \((-1, 4)\) and the slope \(7\) into the equation.
  3. Solve for \( y \) to get the equation in slope-intercept form.
Step 1: Identify the Given Information

We are given a point \((-1, 4)\) and a slope \(m = 7\). We need to find the equation of the line in slope-intercept form, which is expressed as \(y = mx + b\).

Step 2: Use the Point-Slope Form

We start with the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Substituting the given point \((-1, 4)\) and the slope \(7\): \[ y - 4 = 7(x + 1) \]

Step 3: Solve for \(y\)

Now, we simplify the equation to solve for \(y\): \[ y - 4 = 7x + 7 \] Adding \(4\) to both sides gives: \[ y = 7x + 11 \]

Final Answer

The equation of the line in slope-intercept form is \[ \boxed{y = 7x + 11} \]

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