MATH SOLVE

4 months ago

Q:
# Which is an equation of a line that passes through the point (-4, 7) and is perpendicular to the line y = (1/2)x + 4

Accepted Solution

A:

Find the slope of the perpendicular line:

[tex]y = \dfrac{1}{2} x + b[/tex]

[tex]\text {Slope = } \dfrac{1}{2} [/tex]

[tex]\text {Slope =} \boxed {\text{negative reciprocal}} \text { of the slope of the original line}[/tex]

[tex]\text {Perpendicular Slope = -2}[/tex]

Form the equation:

[tex]y = mx + b[/tex]

[tex]y = -2x + b[/tex]

Find y-intercept given that the line passed through (-4, 7):

[tex]y = -2x + b[/tex]

[tex]7 = -2(-4) + b[/tex]

[tex]7 = 8 + b[/tex]

[tex]b = 7 - 8[/tex]

[tex]b = -1[/tex]

Form the equation:

[tex]y = -2x - 1[/tex]

[tex]\boxed {\boxed {Answer: y = -2x - 1}}[/tex]

[tex]y = \dfrac{1}{2} x + b[/tex]

[tex]\text {Slope = } \dfrac{1}{2} [/tex]

[tex]\text {Slope =} \boxed {\text{negative reciprocal}} \text { of the slope of the original line}[/tex]

[tex]\text {Perpendicular Slope = -2}[/tex]

Form the equation:

[tex]y = mx + b[/tex]

[tex]y = -2x + b[/tex]

Find y-intercept given that the line passed through (-4, 7):

[tex]y = -2x + b[/tex]

[tex]7 = -2(-4) + b[/tex]

[tex]7 = 8 + b[/tex]

[tex]b = 7 - 8[/tex]

[tex]b = -1[/tex]

Form the equation:

[tex]y = -2x - 1[/tex]

[tex]\boxed {\boxed {Answer: y = -2x - 1}}[/tex]