Chapter 3: Q 3.6. (page 286)

Find an equation of a line parallel to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ . Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation is $y = \frac{1}{2} x + 1$ .

Step by step solution

Step 1. Find the slope of the given line

The given line is $y = \frac{1}{2} x - 3$ .

The line is already in the slope-intercept form.

Therefore the slope is:

$m = \frac{1}{2}$

Step 2. Find the slope of the parallel line and identify the point

As we know that parallel lines have the same slope.

Therefore the slope of the parallel line is also $\frac{1}{2}$ .

The given point is $(6, 4)$ .

$(x_{1}, y_{1}) = (6, 4)$

Step 3. Substitute the values into the point-slope form

The point-slope form is:

$y - y_{1} = m (x - x_{1}) y - 4 = \frac{1}{2} (x - 6) y - 4 = \frac{1}{2} x - 3$

Step 4. Write the equation in slope-intercept form

The slope-intercept form of the equation is $y = \frac{1}{2} x + 1$ .

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Find an equation of a line parallel to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ . Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Find the slope of the given line

Step 2. Find the slope of the parallel line and identify the point

Step 3. Substitute the values into the point-slope form

Step 4. Write the equation in slope-intercept form

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Find an equation of a line parallel to the line y=12x-3that contains the point (6,4). Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Find the slope of the given line

Step 2. Find the slope of the parallel line and identify the point

Step 3. Substitute the values into the point-slope form

Step 4. Write the equation in slope-intercept form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Find an equation of a line parallel to the line $y = \frac{1}{2} x - 3$ that contains the point $(6, 4)$ . Write the equation in slope-intercept form.