Join the IDNLearn.com community and start exploring a world of knowledge today. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.
Write the slope-intercept form of the equation of the line through the given point with the given slope.
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.
