A. Characterized the x-intercept and the y-intercept of the given linear equatio

aortiH

aortiH

Answered question

2021-09-16

A. Characterized the x-intercept and the y-intercept of the given linear equations below. Then use them to draw and characterized the graph of the linear equation.
Note: characterized means to tell whether the slope of the line is positive or negative and to tell whether the line is pointing upward to the right or downward to the right.
1. 6x+3y=18
2. 3x+2y=9x+12

Answer & Explanation

curwyrm

curwyrm

Skilled2021-09-17Added 87 answers

Step 1
(A) Given,
1. 6x+3y=18
2. 3x+2y=9x+12
As we know,
Y-intercept form of Linear Equation,
y=mx+c ....... (1)
Where,
m= slope of Line
c= y-intercept
Also,
If we put x=0 in Linear Equation and we get the y-intercept value.
and If we put y=0 in Linear Equation and we get x-intercept Value.
If Slope is Positive then Line is pointing upward to the Right.
If Slope is Negative then Line is Pointing Downward to the Right.
Step 2
1. 6x+3y=18
Add 6x both Sides,
6x+3y+6x=18+6x
3y=6x18
Divide Both sides by 3,
3y3=6x183
y=2x6 .........(2)
Compare this equation with (1)
we get,
m=slope=2 and c=6= y-intercept
If we put y=0 in equation (2)
0=2x6
2x=6
x=3
Here x-intercept is 3
Here,
The slope is Positive Hence line Is Pointing Upward to the right.
x-intercept =3
y-intercept =6
The Line is Pointing Upwardto the Right.
Step 3
2. 3x+2y=9x+12
Subtract 3x both Sides,
3x+2y3x=9x+123x
2y=6x+12
Divide Both sides by 2,
2y2=6x+122
y=3x+6 ...........(3)
Compare this equation with (1)
we get,
m=slope=3 and c=6= y-intercept
If we put y=0 in equation (2)
0=3x+6
3x=6
x=3
Here x-intercept is -3
Here,
The slope is Positive Hence line Is Pointing Upward to the right.
Answer:
x-intercept =3
y-intercept =6
The Line is Pointing Upward to the Right.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?