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 equation 5x+4y=15x+4y=1 is graphed in the xyxy-plane. Which of the following is a true statement about the graph?\newlineChoose 11 answer:\newline(A) The graph's yy-intercept is 15\frac{1}{5}.\newline(B) The graph's xx-intercept is −14-\frac{1}{4}.\newline(C) The graph has a slope of −54-\frac{5}{4}.\newline(D) The graph has a slope of −45-\frac{4}{5}.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Function transformation rulesright chevron icon

Full solution

Q. The equation 5x+4y=15x+4y=1 is graphed in the xyxy-plane. Which of the following is a true statement about the graph?\newlineChoose 11 answer:\newline(A) The graph's yy-intercept is 15\frac{1}{5}.\newline(B) The graph's xx-intercept is −14-\frac{1}{4}.\newline(C) The graph has a slope of −54-\frac{5}{4}.\newline(D) The graph has a slope of −45-\frac{4}{5}.
  1. Finding the y-intercept: To find the y-intercept, we set xx to 00 and solve for yy.
    5(0)+4y=15(0) + 4y = 1
    4y=14y = 1
    y=14y = \frac{1}{4}
    The y-intercept is the point where the graph crosses the y-axis, which is at (0,y)(0, y).
  2. Finding the x-intercept: To find the x-intercept, we set yy to 00 and solve for xx.
    5x+4(0)=15x + 4(0) = 1
    5x=15x = 1
    x=15x = \frac{1}{5}
    The x-intercept is the point where the graph crosses the x-axis, which is at (x,0)(x, 0).
  3. Finding the slope of the graph: To find the slope of the graph, we can rewrite the equation in slope-intercept form y=mx+by = mx + b, where mm is the slope.4y=−5x+14y = -5x + 1y=(−5/4)x+1/4y = (-5/4)x + 1/4The slope of the graph is the coefficient of xx, which is −5/4-5/4.

More problems from Function transformation rules

Question
Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=9∣x+2∣−4f(x)=9|x+2|-4.\newlineChoices:\newline(A)g(x)=9∣x+2∣−4]\text{}(A)g(x) = 9|x+2| - 4\text{]}\newline(B)g(x)=9∣x−2∣−4]\text{}(B)g(x) = 9|x-2| - 4\text{]}\newline(C)g(x)=−9∣x−2∣+4]\text{}(C)g(x)=-9|x-2| +4\text{]}\newline(D)g(x)=−9∣x+2∣+4]\text{(D)}g(x) = -9|x + 2| + 4\text{]}
Get tutor helpright-arrow

Posted 2 months ago

Question
What does the transformation f(x)↦f(x−4) f(x) \mapsto f(x - 4) do to the graph of f(x) f(x) ?\newlineChoices:\newline(A) translates it 4 units right\text{translates it } 4 \text{ units right}\newline(B) translates it 4 units down\text{translates it } 4 \text{ units down}\newline(C) translates it 4 units left\text{translates it } 4 \text{ units left}\newline(D) translates it 4 units up\text{translates it } 4 \text{ units up}
Get tutor helpright-arrow

Posted 2 months ago

Question
What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically
Get tutor helpright-arrow

Posted 1 month ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 99 units down of f(x)=10x+8f(x) = 10x + 8.\newlineChoices:\newline(A) g(x)=10x−82g(x) = 10x - 82 \newline(B) g(x)=10x+98g(x) = 10x + 98 \newline(C) g(x)=10x−1g(x) = 10x - 1\newline(D) g(x)=10x+17g(x) = 10x + 17
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}
Get tutor helpright-arrow

Posted 1 month ago

Question
The parabola y=x2y=x^{2} is scaled vertically by a factor of 77. What is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 4 months ago

Question
The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 4 months ago

Question
The parabola y=x2y=x^{2} is shifted up by 22 units and to the right by 33 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 1 month ago

Question
The parabola y=x2 y=x^{2} is reflected across the x x -axis and then scaled vertically by a factor of 55 .\newlineWhat is the equation of the new parabola?\newliney=□ y=\square
Get tutor helpright-arrow

Posted 2 months ago

Question
The parabola y=x2 y=x^{2} is scaled vertically by a factor of 110 \frac{1}{10} .\newlineWhat is the equation of the new parabola?\newliney= y=
Get tutor helpright-arrow

Posted 3 months ago

View all (18)