IDNLearn.com: Where your questions meet expert answers and community support. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.
Sagot :
Sure, let's work through this problem step-by-step to find the slope-intercept form of the equation of the line.
### Step 1: Understand the problem
We are given:
- A point through which the line passes: [tex]\((3, -5)\)[/tex]
- The slope of the line: [tex]\( -\frac{2}{3} \)[/tex]
### Step 2: Recall the slope-intercept form
The slope-intercept form of the equation of a line is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept
### Step 3: Substitute the slope and the point into the equation
We need to find the y-intercept [tex]\((b)\)[/tex]. To do this, we use the given point [tex]\((x_1, y_1) = (3, -5)\)[/tex] and the slope [tex]\( m = -\frac{2}{3} \)[/tex].
Substitute the given point and the slope into the slope-intercept form:
[tex]\[ y_1 = mx_1 + b \][/tex]
[tex]\[ -5 = -\frac{2}{3} \cdot 3 + b \][/tex]
### Step 4: Solve for [tex]\( b \)[/tex]
First, simplify the multiplication:
[tex]\[ -5 = -2 + b \][/tex]
Then, solve for [tex]\( b \)[/tex]:
[tex]\[ -5 + 2 = b \][/tex]
[tex]\[ b = -3 \][/tex]
### Step 5: Write the final equation
Now that we have the y-intercept [tex]\( b = -3 \)[/tex] and the slope [tex]\( m = -\frac{2}{3} \)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[ y = -\frac{2}{3} x - 3 \][/tex]
### Final Answer
The equation of the line in slope-intercept form is:
[tex]\[ y = -\frac{2}{3}x - 3 \][/tex]
### Step 1: Understand the problem
We are given:
- A point through which the line passes: [tex]\((3, -5)\)[/tex]
- The slope of the line: [tex]\( -\frac{2}{3} \)[/tex]
### Step 2: Recall the slope-intercept form
The slope-intercept form of the equation of a line is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept
### Step 3: Substitute the slope and the point into the equation
We need to find the y-intercept [tex]\((b)\)[/tex]. To do this, we use the given point [tex]\((x_1, y_1) = (3, -5)\)[/tex] and the slope [tex]\( m = -\frac{2}{3} \)[/tex].
Substitute the given point and the slope into the slope-intercept form:
[tex]\[ y_1 = mx_1 + b \][/tex]
[tex]\[ -5 = -\frac{2}{3} \cdot 3 + b \][/tex]
### Step 4: Solve for [tex]\( b \)[/tex]
First, simplify the multiplication:
[tex]\[ -5 = -2 + b \][/tex]
Then, solve for [tex]\( b \)[/tex]:
[tex]\[ -5 + 2 = b \][/tex]
[tex]\[ b = -3 \][/tex]
### Step 5: Write the final equation
Now that we have the y-intercept [tex]\( b = -3 \)[/tex] and the slope [tex]\( m = -\frac{2}{3} \)[/tex], we can write the equation of the line in slope-intercept form:
[tex]\[ y = -\frac{2}{3} x - 3 \][/tex]
### Final Answer
The equation of the line in slope-intercept form is:
[tex]\[ y = -\frac{2}{3}x - 3 \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.