Q11. 11. Write an equation in slope-i... [FREE SOLUTION]

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

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

– 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 $(a, b) = (0, 7)$ .

– 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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91影视

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

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

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