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Chapter 2: Q19. (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 $y = \frac{4}{5} x$ .

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 the origin $(0, 0)$ and $(2.5, 2)$ .

Then, $(h, k) = (0, 0)$ and $(a, b) = (2.5, 2)$ .

03

– Write the equation

Put $(h, k) = (0, 0)$ and $(a, b) = (2.5, 2)$ in $\frac{y - k}{x - h} = \frac{b - k}{a - h}$ to get,

$\frac{y - 0}{x - 0} = \frac{2 - 0}{2.5 - 0}$

$\frac{y}{x} = \frac{2}{2.5}$ (Simplify)

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

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

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

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

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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.

$41.3 x - 4 y - 10 = 0$

Which of the equations $x + 9 y = 7, x^{2} + 5 y = 0,$ and $y = 3 x - 1$ is not linear?

Find each value if $f (x) = 5 x - 9$

$f (6)$

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

$- \frac{1}{5} y = x + 4$

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

$0.5 x = - 0.2 y - 0.4$

See all solutions

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