Which equation best represents the line that is parallel to 3x -4y=7 and passes through the point (-4,-2)? Select two options.

Mathematics

1 answer:

katovenus [111]2 years ago

6 0

Answer:

The equation that best represents the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2) is y = 3/4x + 1.

Step-by-step explanation:

3x - 4y = 7 and (-4, -2)

First, solve for y in the equation:

3x - 4y = 7

-4y = -3x + 7

4y = 3x - 7

y = 3/4x - 7/4

m = 3/4 (This will be the slope of the parallel line.) and (-4, -2)

Use the point-slope equation to find the equation that will best represent a parallel line:

y − y1 = m(x − x1)

y - -2 = 3/4(x - -4)

y + 2 = 3/4x + 3 (the 4s cancel out)

(3/4 x 4/1 = 3)

y = 3/4x + 1

The graph that I attached is what these two equations would look like graphed. I am not sure what you mean by two options, I'm sorry!

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The equation line l is given by the equation y= 7/4x+3. line m goes through the point ( –1,4) and is perpendicular to line l whi

mr_godi [17]

We determine line m as follows:

*First, by theorem we have the following:

$m_1=-\frac{1}{m_2}$

Here m1 & m2 are the slopes of two perpendicular lines. For all lines that are perpendicular that is true, so we calculate the slope of line m using the slope of the function given [Which has a slope of 7/4]:

$m_1=-\frac{1}{\frac{7}{4}}\Rightarrow m_1=-\frac{4}{7}$

So, the slope of line m is -4/7. Now, using this slope and the point (-1, 4) we replace in the following expression:

$y-y_1=m_1(x-x_1)$

Here x1, y1 & m1 are the x-component of the point, the y-component of the point, and the slope of the line respectively, so we replace and solve for y: