Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find the equation of the line perpendicular to [tex]\( y = -\frac{1}{2}x - 5 \)[/tex] that passes through the point [tex]\( (2, 7) \)[/tex], follow these steps:
1. Identify the slope of the given line: The given line is in slope-intercept form [tex]\( y = mx + b \)[/tex]. Here, [tex]\( m = -\frac{1}{2} \)[/tex].
2. Find the slope of the perpendicular line: For a line to be perpendicular to another, its slope must be the negative reciprocal of the original slope. The negative reciprocal of [tex]\( -\frac{1}{2} \)[/tex] is 2.
Therefore, the slope of the perpendicular line is [tex]\( m = 2 \)[/tex].
3. Use the slope-intercept form equation [tex]\( y = mx + b \)[/tex]: We now have the slope [tex]\( m = 2 \)[/tex] and need to find the y-intercept [tex]\( b \)[/tex]. We will use the point [tex]\( (2, 7) \)[/tex] which the line passes through.
4. Substitute the point into the equation: Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 7 \)[/tex] into the slope-intercept form equation to solve for [tex]\( b \)[/tex]:
[tex]\[ 7 = 2(2) + b \][/tex]
5. Solve for [tex]\( b \)[/tex]:
[tex]\[ 7 = 4 + b \][/tex]
[tex]\[ b = 3 \][/tex]
6. Write the equation of the line: Now that we have the slope [tex]\( m = 2 \)[/tex] and the y-intercept [tex]\( b = 3 \)[/tex], the equation of the line is:
[tex]\[ y = 2x + 3 \][/tex]
Therefore, the equation of the line perpendicular to [tex]\( y = -\frac{1}{2} x - 5 \)[/tex] that passes through the point [tex]\( (2, 7) \)[/tex] is:
[tex]\[ y = 2x + 3 \][/tex]
1. Identify the slope of the given line: The given line is in slope-intercept form [tex]\( y = mx + b \)[/tex]. Here, [tex]\( m = -\frac{1}{2} \)[/tex].
2. Find the slope of the perpendicular line: For a line to be perpendicular to another, its slope must be the negative reciprocal of the original slope. The negative reciprocal of [tex]\( -\frac{1}{2} \)[/tex] is 2.
Therefore, the slope of the perpendicular line is [tex]\( m = 2 \)[/tex].
3. Use the slope-intercept form equation [tex]\( y = mx + b \)[/tex]: We now have the slope [tex]\( m = 2 \)[/tex] and need to find the y-intercept [tex]\( b \)[/tex]. We will use the point [tex]\( (2, 7) \)[/tex] which the line passes through.
4. Substitute the point into the equation: Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 7 \)[/tex] into the slope-intercept form equation to solve for [tex]\( b \)[/tex]:
[tex]\[ 7 = 2(2) + b \][/tex]
5. Solve for [tex]\( b \)[/tex]:
[tex]\[ 7 = 4 + b \][/tex]
[tex]\[ b = 3 \][/tex]
6. Write the equation of the line: Now that we have the slope [tex]\( m = 2 \)[/tex] and the y-intercept [tex]\( b = 3 \)[/tex], the equation of the line is:
[tex]\[ y = 2x + 3 \][/tex]
Therefore, the equation of the line perpendicular to [tex]\( y = -\frac{1}{2} x - 5 \)[/tex] that passes through the point [tex]\( (2, 7) \)[/tex] is:
[tex]\[ y = 2x + 3 \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.