Get the most out of your questions with IDNLearn.com's extensive resources. Join our interactive community and access reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
To find the equation of a line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the line [tex]\(y = 3x - 4\)[/tex], we can follow these steps:
### Step 1: Identify the Slope
First, we need to know that lines that are parallel have the same slope. The given line has the equation [tex]\(y = 3x - 4\)[/tex], and the slope (denoted as [tex]\(m\)[/tex]) of this line is the coefficient of [tex]\(x\)[/tex], which is [tex]\(3\)[/tex].
### Step 2: Use the Point-Slope Form
Next, we use the point-slope form of the equation of a line, which is given by:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is the given point [tex]\((3, 2)\)[/tex] and [tex]\(m\)[/tex] is the slope [tex]\(3\)[/tex].
Plugging in the values, we get:
[tex]\[y - 2 = 3(x - 3)\][/tex]
### Step 3: Solve for [tex]\(y\)[/tex]
To find the equation in slope-intercept form ([tex]\(y = mx + b\)[/tex]), we solve for [tex]\(y\)[/tex]:
[tex]\[y - 2 = 3(x - 3)\][/tex]
[tex]\[y - 2 = 3x - 9\][/tex]
[tex]\[y = 3x - 9 + 2\][/tex]
[tex]\[y = 3x - 7\][/tex]
### Conclusion
Thus, the equation of the line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the line [tex]\(y = 3x - 4\)[/tex] is:
[tex]\[ \boxed{y = 3x - 7} \][/tex]
### Step 1: Identify the Slope
First, we need to know that lines that are parallel have the same slope. The given line has the equation [tex]\(y = 3x - 4\)[/tex], and the slope (denoted as [tex]\(m\)[/tex]) of this line is the coefficient of [tex]\(x\)[/tex], which is [tex]\(3\)[/tex].
### Step 2: Use the Point-Slope Form
Next, we use the point-slope form of the equation of a line, which is given by:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is the given point [tex]\((3, 2)\)[/tex] and [tex]\(m\)[/tex] is the slope [tex]\(3\)[/tex].
Plugging in the values, we get:
[tex]\[y - 2 = 3(x - 3)\][/tex]
### Step 3: Solve for [tex]\(y\)[/tex]
To find the equation in slope-intercept form ([tex]\(y = mx + b\)[/tex]), we solve for [tex]\(y\)[/tex]:
[tex]\[y - 2 = 3(x - 3)\][/tex]
[tex]\[y - 2 = 3x - 9\][/tex]
[tex]\[y = 3x - 9 + 2\][/tex]
[tex]\[y = 3x - 7\][/tex]
### Conclusion
Thus, the equation of the line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the line [tex]\(y = 3x - 4\)[/tex] is:
[tex]\[ \boxed{y = 3x - 7} \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.