Chapter 2: Q. 29. (page 79)

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
passes through $(- 2, 5)$ and $(3, 1)$

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = - \frac{4}{5} x + \frac{17}{5}$ .

Step by step solution

Step 1. State the concept

The slope intercept form of a straight-line equation is $y = m x + c$ where m is the slope and c is the y-intercept.

The equation of a straight-line passing through the points $(h, k)$ and $(a, b)$ is given as $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ .

Step 2. List the given data

It is given that the line passes through $(- 2, 5)$ and $(3, 1)$ .

Then, $(h, k) = (- 2, 5)$ and $(a, b) = (3, 1)$ .

Step 3. Write the equation

Put $(h, k) = (- 2, 5)$ and $(a, b) = (3, 1)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - 5}{x - (- 2)} = \frac{1 - 5}{3 - (- 2)}$

$\frac{y - 5}{x + 2} = \frac{- 4}{3 + 2}$ (Simplify)

$\frac{y - 5}{x + 2} = - \frac{4}{5}$ (Simplify)

$\frac{y - 5}{x + 2} (x + 2) = - \frac{4}{5} (x + 2)$ (Multiply both sides by $x + 2$ )

$y - 5 = - \frac{4}{5} (x + 2)$ (Simplify)

$y - 5 = - \frac{4}{5} x - \frac{8}{5}$ (Distributive property)

$y - 5 + 5 = - \frac{4}{5} x - \frac{8}{5} + 5$ (Add 5 to both sides)

$y = - \frac{4}{5} x + \frac{17}{5}$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y = - \frac{4}{5} x + \frac{17}{5}$ .

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Column A	Column B
$\frac{1}{4}$	$\frac{1}{m} - \frac{1}{4}$

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
passes through $(- 2, 5)$ and $(3, 1)$

Short Answer

Step by step solution

Step 1. State the concept

Step 2. List the given data

Step 3. Write the equation

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Write an equation in slope-intercept form for the line that satisfies each set of conditions.passes through -2,5 and 3,1

Short Answer

Step by step solution

Step 1. State the concept

Step 2. List the given data

Step 3. Write the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Statistics

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
passes through $(- 2, 5)$ and $(3, 1)$