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Chapter 2: Q11. (page 78)

11. Write an equation in slope-intercept form for the graph at the right.

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = \frac{5}{4} x + 7$ .

Step by step solution

01

– 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 $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ .

02

– List the given data

It is clear, from the graph, that the line passes through $(- 4, 2)$ and $(0, 7)$ .

Then, $(h, k) = (- 4, 2)$ and $(a, b) = (0, 7)$ .

03

– Write the equation

Put $(h, k) = (- 4, 2)$ and $(a, b) = (0, 7)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - 2}{x - (- 4)} = \frac{7 - 2}{0 - (- 4)}$

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

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

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

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

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

$y = \frac{5}{4} x + 7$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y = \frac{5}{4} x + 7$ .

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Most popular questions from this chapter

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.

$2 x + 5 y - 10 = 0$

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.

$19 . g (x) = 10 + \frac{2}{x^{2}}$

Answer the question that was posed at the beginning of the lesson.

How do linear equations relate to time spent studying?

Include the following in your answer:

why only the part of the graph in the first quadrant is shown, and

an interpretation of the graph's intercepts in terms of the amount of time

Lolita spends on each subject.

If $\bar{A C}$ is 2 units, what is the value of $t$ ?

62. Which function is linear

$(A) f (x) = x^{2}$

$(B) g (x) = 2.7$

$(C) g (x) = \sqrt{x - 1}$

$(D) f (x) = \sqrt{9 - x^{2}}$

See all solutions

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