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:

The graph of a line in the xy-plane has a slope of 4 and contains the point (1,-5). The graph of a second line passes through the points (0,4) and (12,0). If the two lines intersect at the point (a,b), what is the value of a-b ? Choose 1 answer: (A) -9 (B) -5 (c) 0 (D) 4

The graph of a line in the xy x y -plane has a slope of 44 and contains the point (1,−5) (1,-5) . The graph of a second line passes through the points (0,4) (0,4) and (12,0) (12,0) . If the two lines intersect at the point (a,b) (a, b) , what is the value of a−b a-b ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −5-5\newline(C) 00\newline(D) 44

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. The graph of a line in the xy x y -plane has a slope of 44 and contains the point (1,−5) (1,-5) . The graph of a second line passes through the points (0,4) (0,4) and (12,0) (12,0) . If the two lines intersect at the point (a,b) (a, b) , what is the value of a−b a-b ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −5-5\newline(C) 00\newline(D) 44
  1. Find First Line Equation: First, let's find the equation of the first line with a slope of 44 that contains the point (1,−5)(1, -5). Using the point-slope form of a line equation: \newliney−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point on the line. \newliney−(−5)=4(x−1)y - (-5) = 4(x - 1)
  2. Simplify First Line Equation: Simplify the equation of the first line:\newliney+5=4x−4y + 5 = 4x - 4\newliney=4x−4−5y = 4x - 4 - 5\newliney=4x−9y = 4x - 9\newlineThis is the equation of the first line.
  3. Find Second Line Equation: Now, let's find the equation of the second line that passes through the points (0,4)(0, 4) and (12,0)(12, 0). We can use the slope formula: \newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} \newlinem=0−412−0m = \frac{0 - 4}{12 - 0} \newlinem=−412m = \frac{-4}{12} \newlinem=−13m = -\frac{1}{3}
  4. Calculate Intersection Point Slope: Using the point-slope form again for the second line with the point (0,4)(0, 4):\newliney−4=(−13)(x−0)y - 4 = \left(-\frac{1}{3}\right)(x - 0)\newliney−4=(−13)xy - 4 = \left(-\frac{1}{3}\right)x\newliney=(−13)x+4y = \left(-\frac{1}{3}\right)x + 4\newlineThis is the equation of the second line.
  5. Find Intersection Point: To find the intersection point (a,b)(a, b), we set the equations of the two lines equal to each other:\newline4x−9=(−13)x+44x - 9 = (-\frac{1}{3})x + 4
  6. Calculate x-coordinate: Solve for xx: \newline4x+(13)x=4+94x + (\frac{1}{3})x = 4 + 9\newline(123)x+(13)x=13(\frac{12}{3})x + (\frac{1}{3})x = 13 \newline(133)x=13(\frac{13}{3})x = 13 \newlinex=13(133)x = \frac{13}{(\frac{13}{3})} \newlinex=13×(313)x = 13 \times (\frac{3}{13}) \newlinex=3x = 3
  7. Calculate y-coordinate: Now that we have the x-coordinate of the intersection point, we can find the y-coordinate by plugging x=3x = 3 into one of the line equations. Let's use the first line's equation:\newliney=4x−9y = 4x - 9\newliney=4(3)−9y = 4(3) - 9\newliney=12−9y = 12 - 9\newliney=3y = 3
  8. Determine Intersection Point: We have found the intersection point (a,b)(a, b) to be (3,3)(3, 3). Now we can find a−ba - b: \newlinea−b=3−3a - b = 3 - 3 \newlinea−b=0a - b = 0

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