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Chapter 2: Q20. (page 78)

Write an equation in slope-intercept form for each graph.

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = - \frac{5}{3} x + \frac{29}{3}$ .

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 $(4, 3)$ and $(7, - 2)$ .

Then, $(h, k) = (4, 3)$ and $(a, b) = (7, - 2)$ .

03

– Write the equation

Put $(h, k) = (4, 3)$ and $(a, b) = (7, - 2)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - 3}{x - 4} = \frac{- 2 - 3}{7 - 4}$

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

$\frac{y - 3}{x - 4} (x - 4) = - \frac{5}{3} (x - 4)$ (Multiply both sides by $x - 4$ )

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

$y - 3 = - \frac{5}{3} x + \frac{20}{3}$ (Distributive property)

$y - 3 + 3 = - \frac{5}{3} x + \frac{20}{3} + 3$ (Add 3 to both sides)

$y = - \frac{5}{3} x + \frac{29}{3}$

So, the required equation of the straight line in slope-intercept form is $y = - \frac{5}{3} x + \frac{29}{3}$ .

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Most popular questions from this chapter

Including a 6% sales tax, a paperback book costs $8.43$ . What is the price before tax?

Write each equation in standard form. Identify A, B and C.

$0.5 x = - 0.2 y - 0.4$

Find the slope of the line that passes through each pair of points

$(5, 7), (4, - 6)$

Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function.

$\{(- 5, 2), (2, 4), (1, 1), (- 5, - 2)\}$

Write each equation in standard form. Identify A, B and C.

$0.5 x = 3$

See all solutions

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