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Without graphing, determine if the two lines are intersecting, parallel or the same line. (If the equation is not in slope-Intercept form, show all work to convert equation to slope-intercept form)
y=4x-5
(a) 8x + y = 3
Intersecting
B parallel
same lines
(b) The system of equation will have one
solution(s).



Answer :

GinnyAnswer
To determine the relation between the two lines, we first need to see if both equations are in slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.

The first equation is already in the slope-intercept form:
[tex]\[ y = 4x - 5 \][/tex]

This equation has a slope of [tex]\( m = 4 \)[/tex] and a y-intercept of [tex]\( b = -5 \)[/tex].

The second equation is:
[tex]\[ 8x + y = 3 \][/tex]

To convert it into slope-intercept form, we isolate [tex]\( y \)[/tex]:
[tex]\[ y = -8x + 3 \][/tex]

Now it's in the slope-intercept form with a slope [tex]\( m = -8 \)[/tex] and y-intercept [tex]\( b = 3 \)[/tex].

The slopes of the two lines are:
- Slope of the first line: [tex]\( m = 4 \)[/tex]
- Slope of the second line: [tex]\( m = -8 \)[/tex]

These slopes are not equal to each other. Since the slopes are different, the lines are neither parallel nor the same line; they are intersecting. This means:
- The two lines are intersecting, which answers part (a).

Now let's consider part (b) regarding the number of solutions:
Because the lines are intersecting, they meet at exactly one point. Therefore, the system of equations will have exactly one solution. Hence for part (b), the answer is:
- The system of equations will have one solution.

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