Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.2, Problem 57SR
To determine

Find the x and y intercepts from the graph of the equation 4x−14y=28 .

Expert Solution & Answer
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Answer to Problem 57SR

The y − Intercept is −2 and the x − Intercept is 7.

Explanation of Solution

Given:

The equation: 4x−14y=28

Concept Used:

The  x -intercepts are where the graph crosses the  x -axis, and the  y -intercepts are where the graph crosses the  y -axis.

Then, algebraically,

  • an  x -intercept is a point on the graph where  y  is zero, and
  • a  y -intercept is a point on the graph where  x  is zero.

More specifically,

  • an  x -intercept is a point in the equation where the  y -value is zero, and
  • a  y -intercept is a point in the equation where the  x -value is zero.

Calculation:

Graph the equation 4x−14y=28

Rewrite the equation y as subject.

  4x−14y=284x−4x−14y=28−4x  [ Subtract  4x  from  both  sides ] −14y=28−4x−14y−14  =  28−14  −  4x−14  [  Divide  each  term  by  −14  ]y  =  −2  +  27xy=   27x−2

Make a table.

    Table Graph y=   27x−2
    x y=   27x−2 f(x) (x, f(x)) 7
    y=   27  ·  7−2  =7−7=0 0 (7, 0 )
    0 y=   27  ·  0−2  =−2 −2 (0, −2 )

    The graph intersects the x- axis at 7, and intersects y – axis is at −2 .

    		Algebra 1, Chapter 3.2, Problem 57SR

Find the x − intercept, look for the point where the line crosses the x − axis.

In the graph there is a point (7, 0) where the line crosses the X − axis,

Find the y − intercept, look for the point where the line crosses the y − axis.

In the graph there is a point (0, −2 ) where the line crosses the y − axis.

The x − Intercept is 7 and the y − Intercept is −2 .

Thus, the x − Intercept is 7 and the y − Intercept is −2 .

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Chapter 3 Solutions

Algebra 1

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