Chapter 2: Q35. (page 79)

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
35. passes through $(4, 6)$ , parallel to the graph of $y = \frac{2}{3} x + 5$

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = \frac{2}{3} x + \frac{10}{3}$ .

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 slopes of parallel lines are equal.

The equation of a straight-line having slope $m$ and passing through the point $(h, k)$ is given as $y - k = m (x - h)$ .

– List the given data

It is given that the line passes through $(4, 6)$ and is parallel to $y = \frac{2}{3} x + 5$ .

Then, $(h, k) = (4, 6)$ .

– Determine the slope

Comparing $y = \frac{2}{3} x + 5$ to $y = m x + c$ , $m = \frac{2}{3}$ .

So, the slope of $y = \frac{2}{3} x + 5$ and thus of the required line, as they are parallel, is $\frac{2}{3}$ .

Then, $m = \frac{2}{3}$ .

– Write the equation

Put $m = \frac{2}{3}$ and $(h, k) = (4, 6)$ in $y - k = m (x - h)$ to get,

$y - 6 = \frac{2}{3} (x - 4)$

$y - 6 = \frac{2}{3} x - \frac{8}{3}$ (Distributive property)

$y - 6 + 6 = \frac{2}{3} x - \frac{8}{3} + 6$ (Add 6 to both sides)

$y = \frac{2}{3} x + \frac{10}{3}$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y = \frac{2}{3} x + \frac{10}{3}$ .

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Write an equation in slope-intercept form for the line that satisfies each set of conditions.
35. passes through $(4, 6)$ , parallel to the graph of $y = \frac{2}{3} x + 5$

Short Answer

Step by step solution

– State the concept

– List the given data

– Determine the slope

– Write the equation

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Write an equation in slope-intercept form for the line that satisfies each set of conditions.35. passes through 4,6, parallel to the graph of y=23x+5

Short Answer

Step by step solution

– State the concept

– List the given data

– Determine the slope

– Write the equation

One App. One Place for Learning.

Most popular questions from this chapter

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Write an equation in slope-intercept form for the line that satisfies each set of conditions.
35. passes through $(4, 6)$ , parallel to the graph of $y = \frac{2}{3} x + 5$