At IDNLearn.com, find answers to your most pressing questions from experts and enthusiasts alike. Ask anything and receive comprehensive, well-informed responses from our dedicated team of experts.
Sagot :
To determine the equation of the line in slope-intercept form that passes through the point [tex]\((4, 5)\)[/tex] and is parallel to the line [tex]\( y = -2x - 2 \)[/tex], we need to follow these steps:
1. Identify the slope of the given line:
The given line is [tex]\( y = -2x - 2 \)[/tex]. In slope-intercept form [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] represents the slope. Therefore, the slope of the given line is [tex]\( m = -2 \)[/tex].
2. Recognize that parallel lines have the same slope:
Since parallel lines have identical slopes, the slope of the new line will also be [tex]\( -2 \)[/tex].
3. Use the slope-intercept form [tex]\( y = mx + b \)[/tex]:
We need to find the y-intercept [tex]\( b \)[/tex] of the new line that passes through the point [tex]\((4, 5)\)[/tex]. We have:
- Slope ([tex]\( m \)[/tex]) is [tex]\( -2 \)[/tex]
- Point [tex]\((x, y)\)[/tex] is [tex]\((4, 5)\)[/tex]
4. Substitute the slope and point into the equation:
Substitute [tex]\( m = -2 \)[/tex], [tex]\( x = 4 \)[/tex], and [tex]\( y = 5 \)[/tex] into the slope-intercept form equation:
[tex]\[ y = mx + b \][/tex]
[tex]\[ 5 = -2(4) + b \][/tex]
5. Solve for [tex]\( b \)[/tex]:
[tex]\[ 5 = -8 + b \][/tex]
Add 8 to both sides to isolate [tex]\( b \)[/tex]:
[tex]\[ 5 + 8 = b \][/tex]
[tex]\[ b = 13 \][/tex]
6. Write the final equation:
The equation of the line in slope-intercept form is:
[tex]\[ y = -2x + 13 \][/tex]
Thus, the equation of the line that passes through the point [tex]\((4, 5)\)[/tex] and is parallel to the line [tex]\( y = -2x - 2 \)[/tex] is:
[tex]\[ y = -2x + 13 \][/tex]
1. Identify the slope of the given line:
The given line is [tex]\( y = -2x - 2 \)[/tex]. In slope-intercept form [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] represents the slope. Therefore, the slope of the given line is [tex]\( m = -2 \)[/tex].
2. Recognize that parallel lines have the same slope:
Since parallel lines have identical slopes, the slope of the new line will also be [tex]\( -2 \)[/tex].
3. Use the slope-intercept form [tex]\( y = mx + b \)[/tex]:
We need to find the y-intercept [tex]\( b \)[/tex] of the new line that passes through the point [tex]\((4, 5)\)[/tex]. We have:
- Slope ([tex]\( m \)[/tex]) is [tex]\( -2 \)[/tex]
- Point [tex]\((x, y)\)[/tex] is [tex]\((4, 5)\)[/tex]
4. Substitute the slope and point into the equation:
Substitute [tex]\( m = -2 \)[/tex], [tex]\( x = 4 \)[/tex], and [tex]\( y = 5 \)[/tex] into the slope-intercept form equation:
[tex]\[ y = mx + b \][/tex]
[tex]\[ 5 = -2(4) + b \][/tex]
5. Solve for [tex]\( b \)[/tex]:
[tex]\[ 5 = -8 + b \][/tex]
Add 8 to both sides to isolate [tex]\( b \)[/tex]:
[tex]\[ 5 + 8 = b \][/tex]
[tex]\[ b = 13 \][/tex]
6. Write the final equation:
The equation of the line in slope-intercept form is:
[tex]\[ y = -2x + 13 \][/tex]
Thus, the equation of the line that passes through the point [tex]\((4, 5)\)[/tex] and is parallel to the line [tex]\( y = -2x - 2 \)[/tex] is:
[tex]\[ y = -2x + 13 \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.