Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following equations represents a line that passes through the points (-3,0) and (9,8) ? I. y=(2)/(3)x+3 II. 4x-6y=-12 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (−3,0) (-3,0) and (9,8) (9,8) ?\newlineI. y=23x+3 y=\frac{2}{3} x+3 \newlineII. 4x−6y=−12 4 x-6 y=-12 \newlineNeither\newlineI only\newlineII only\newlineI and II

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. Which of the following equations represents a line that passes through the points (−3,0) (-3,0) and (9,8) (9,8) ?\newlineI. y=23x+3 y=\frac{2}{3} x+3 \newlineII. 4x−6y=−12 4 x-6 y=-12 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Question Prompt: Question prompt: Which of the following equations represents a line that passes through the points (−3,0)(-3,0) and (9,8)(9,8)?
  2. Calculate Slope: First, let's find the slope mm of the line that passes through the points (−3,0)(-3,0) and (9,8)(9,8) using the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  3. Check Equation I: Using the points (−3,0)(-3,0) and (9,8)(9,8), we calculate the slope as follows:\newlinem=8−09−(−3)=812=23.m = \frac{8 - 0}{9 - (-3)} = \frac{8}{12} = \frac{2}{3}.
  4. Check Equation I: Now, let's check equation I, y=23x+3y = \frac{2}{3}x + 3, to see if it passes through both points. We will substitute the xx-values of the points into the equation and see if we get the corresponding yy-values.
  5. Check Equation II: For point (−3,0)(-3,0), substituting x=−3x = -3 into equation I gives us y=(23)(−3)+3=−2+3=1y = \left(\frac{2}{3}\right)(-3) + 3 = -2 + 3 = 1. This does not equal the yy-value of the point, which is 00. Therefore, equation I does not pass through the point (−3,0)(-3,0).
  6. Rewrite Equation II: For point (9,8)(9,8), substituting x=9x = 9 into equation I gives us y=(23)(9)+3=6+3=9y = \left(\frac{2}{3}\right)(9) + 3 = 6 + 3 = 9. This does not equal the yy-value of the point, which is 88. Therefore, equation I does not pass through the point (9,8)(9,8).
  7. Check Equation II: Now, let's check equation II, 4x−6y=−124x - 6y = -12. We can rewrite this equation in slope-intercept form (y=mx+by = mx + b) to make it easier to compare with the slope we found earlier.
  8. Check Equation II: To rewrite equation II in slope-intercept form, we solve for yy:4x−6y=−124x - 6y = -12−6y=−4x−12-6y = -4x - 12y=(46)x+2y = \left(\frac{4}{6}\right)x + 2y=(23)x+2.y = \left(\frac{2}{3}\right)x + 2.
  9. Check Equation II: To rewrite equation II in slope-intercept form, we solve for yy:
    4x−6y=−124x - 6y = -12
    −6y=−4x−12-6y = -4x - 12
    y=46x+2y = \frac{4}{6}x + 2
    y=23x+2y = \frac{2}{3}x + 2.Now, let's check if equation II in the form y=23x+2y = \frac{2}{3}x + 2 passes through both points. We will substitute the xx-values of the points into the equation and see if we get the corresponding yy-values.
  10. Check Equation II: To rewrite equation II in slope-intercept form, we solve for yy:
    4x−6y=−124x - 6y = -12
    −6y=−4x−12-6y = -4x - 12
    y=46x+2y = \frac{4}{6}x + 2
    y=23x+2y = \frac{2}{3}x + 2.Now, let's check if equation II in the form y=23x+2y = \frac{2}{3}x + 2 passes through both points. We will substitute the xx-values of the points into the equation and see if we get the corresponding yy-values.For point (−3,0)(-3,0), substituting x=−3x = -3 into equation II gives us 4x−6y=−124x - 6y = -1200. This equals the yy-value of the point, which is 4x−6y=−124x - 6y = -1222. Therefore, equation II passes through the point (−3,0)(-3,0).
  11. Check Equation II: To rewrite equation II in slope-intercept form, we solve for yy:
    4x−6y=−124x - 6y = -12
    −6y=−4x−12-6y = -4x - 12
    y=46x+2y = \frac{4}{6}x + 2
    y=23x+2y = \frac{2}{3}x + 2.Now, let's check if equation II in the form y=23x+2y = \frac{2}{3}x + 2 passes through both points. We will substitute the xx-values of the points into the equation and see if we get the corresponding yy-values.For point (−3,0)(-3,0), substituting x=−3x = -3 into equation II gives us 4x−6y=−124x - 6y = -1200. This equals the yy-value of the point, which is 4x−6y=−124x - 6y = -1222. Therefore, equation II passes through the point (−3,0)(-3,0).For point 4x−6y=−124x - 6y = -1244, substituting 4x−6y=−124x - 6y = -1255 into equation II gives us 4x−6y=−124x - 6y = -1266. This equals the yy-value of the point, which is 4x−6y=−124x - 6y = -1288. Therefore, equation II passes through the point 4x−6y=−124x - 6y = -1244.

More problems from Write a quadratic function from its x-intercepts and another point

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 4 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

View all (99)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant