Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The graph of 
(x)/( 2.6)-(y)/( 7.8)=1 in the 
xy-plane is a line. Which of the following is true about this line?
Choose 1 answer:
(A) The graph's 
x-intercept is 2.6 and its 
y-intercept is 7.8.
(B) The graph's 
x-intercept is 2.6 and its 
y-intercept is -7.8 .
(C) The graph has a slope of 2.6.
(D) The graph has a slope of 7.8.

The graph of x2.6y7.8=1 \frac{x}{2.6}-\frac{y}{7.8}=1 in the xy x y -plane is a line. Which of the following is true about this line?\newlineChoose 11 answer:\newline(A) The graph's x x -intercept is 22.66 and its y y -intercept is 77.88 .\newline(B) The graph's x x -intercept is 22.66 and its y y -intercept is 7-7.88 .\newline(C) The graph has a slope of 22.66 .\newlineD The graph has a slope of 77.88 .

Full solution

Q. The graph of x2.6y7.8=1 \frac{x}{2.6}-\frac{y}{7.8}=1 in the xy x y -plane is a line. Which of the following is true about this line?\newlineChoose 11 answer:\newline(A) The graph's x x -intercept is 22.66 and its y y -intercept is 77.88 .\newline(B) The graph's x x -intercept is 22.66 and its y y -intercept is 7-7.88 .\newline(C) The graph has a slope of 22.66 .\newlineD The graph has a slope of 77.88 .
  1. Convert to slope-intercept form: Convert the given equation to slope-intercept form y=mx+by = mx + b.\newlineThe given equation is x2.6y7.8=1\frac{x}{2.6} - \frac{y}{7.8} = 1. To convert it to slope-intercept form, we need to solve for yy.
  2. Isolate y-term: Isolate the yy-term on one side of the equation.\newlineWe can start by adding y7.8\frac{y}{7.8} to both sides of the equation to get x2.6=y7.8+1\frac{x}{2.6} = \frac{y}{7.8} + 1.
  3. Multiply by 77.88: Multiply both sides of the equation by 7.87.8 to eliminate the fraction for yy.\newline7.8×x2.6=y+7.8×17.8 \times \frac{x}{2.6} = y + 7.8 \times 1
  4. Simplify equation: Simplify the equation.\newline7.82.6×x=y+7.8\frac{7.8}{2.6} \times x = y + 7.8\newline3×x=y+7.83 \times x = y + 7.8
  5. Write in slope-intercept form: Write the equation in slope-intercept form.\newliney=3x7.8y = 3x - 7.8
  6. Identify slope and y-intercept: Identify the slope and y-intercept from the equation.\newlineThe slope mm is 33, and the y-intercept bb is 7.8-7.8.
  7. Determine x-intercept: Determine the x-intercept by setting yy to 00 in the equation.0=3x7.80 = 3x - 7.83x=7.83x = 7.8x=7.83x = \frac{7.8}{3}x=2.6x = 2.6
  8. Match with options: Match the findings with the given options.\newlineThe xx-intercept is 2.62.6, and the yy-intercept is 7.8-7.8, which corresponds to option (B). The slope is 33, which is not one of the options provided.

More problems from Slopes of parallel and perpendicular lines