Mathematics High School

What is an equation of the line that is parallel to the one shown and passes through (6, −5)?

A. y=−23x−1
B. y=32x−4
C. y=23x+1
D. y=−32x+4

What Is An Equation Of The Line That Is Parallel To The One Shown And Passes Through (6, 5)? A. Y=23x1

Answers

Answer 1

Answer:

D is the answer

Answer 2

The equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. [tex]\mathbf{y = -\frac{3}{2} x + 4}[/tex]

Recall:

Slope of two lines that are parallel to each other will always be the same value.Slope = rise/run

From the graph shown, the slope (m) of the line is [tex]-\frac{3}{2}[/tex].

Thus, the line that passes through (6, -5) and is parallel to the line in the graph will have the same slope of [tex]-\frac{3}{2}[/tex].

Write the equation in point-slope form by substituting (a, b) = (6, -5) and m = -3/2 into y - b = m(x - a).

Thus:

[tex]y - (-5) = -\frac{3}{2} (x - 6)\\\\y +5 = -\frac{3}{2} (x - 6)[/tex]

Rewrite in point-slope form as y = mx + b

[tex]y +5 = -\frac{3}{2} (x - 6)\\\\y + 5 = -\frac{3}{2} x + 9\\\\y = -\frac{3}{2} x + 9 - 5\\\\\mathbf{y = -\frac{3}{2} x + 4}[/tex]

Therefore, the equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. [tex]\mathbf{y = -\frac{3}{2} x + 4}[/tex]

Learn more here:

https://brainly.com/question/16732089

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