Step-by-step explanation:
1. We are given that slope is 4/3 and y-intercept is -3.
Now, the general form of a straight line is y = mx + c where m is the slope and c is the y-intercept.
So, in our case, the equation of the line is [tex]y = \frac{4x}{3} -3[/tex].
Now, substituting x=0 and y=0, we get the pair of points (x,y) = (0,-3) , ([tex]\frac{9}{4}[/tex],0).
So, plotting these points on a graph and joining them gives the required line as seen in graph 1 below.
We have, the slope intercept form of the line is [tex]y = \frac{4x}{3} -3[/tex].
2. We have the inequality 6x + 2y > 4.
In order to find the solution area, we will use the 'Zero Test' i.e. substitute x=0 and y=0. If the inequality is true, the shaded area is towards the origin and if its false, the shaded area is away from the origin.
Now, we have 6x + 2y > 4 → 0 > 4 which is false. So, the solution region is away from the origin as seen in the graph 2 below.
3. We have the equation 9x - 3y = 12.
A) The slope intercept form is y = 3x - 4.
Because, 9x - 3y = 12 → 3y = 9x - 12 → y = 3x - 4.
B) Now comparing y = 3x - 4 by the general form of a straight line, we see that slope of this line is 3 and y-intercept is -4.
C) We have to find the equation of line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ).
As the lines are perpendicular, the slopes have the relation,
[tex]m_{1} \times m_{2} = -1[/tex]
i.e. [tex]3 \times m_{2} = -1[/tex]
i.e. [tex]m_{2} = \frac{-1}{3}[/tex]
Now, using this slope [tex]m_{2} = \frac{-1}{3}[/tex] and the point ( 3,5 ) , we will find the equation of the line using the formula,
[tex](y - y_{1}) = m \times (x - x_{1})[/tex]
i.e. [tex](y - 5) = \frac{-1}{3} \times (x - 3)[/tex]
i.e. [tex]3y - 15 = -x +3[/tex]
i.e. [tex]x + 3y = 18[/tex]
So, the line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ) is [tex]x + 3y = 18[/tex].
Answer:
1. We are given that slope is 4/3 and y-intercept is -3.
Now, the general form of a straight line is y = mx + c where m is the slope and c is the y-intercept.
So, in our case, the equation of the line is .
Now, substituting x=0 and y=0, we get the pair of points (x,y) = (0,-3) , (,0).
So, plotting these points on a graph and joining them gives the required line as seen in graph 1 below.
We have, the slope intercept form of the line is .
2. We have the inequality 6x + 2y > 4.
In order to find the solution area, we will use the 'Zero Test' i.e. substitute x=0 and y=0. If the inequality is true, the shaded area is towards the origin and if its false, the shaded area is away from the origin.
Now, we have 6x + 2y > 4 → 0 > 4 which is false. So, the solution region is away from the origin as seen in the graph 2 below.
3. We have the equation 9x - 3y = 12.
A) The slope intercept form is y = 3x - 4.
Because, 9x - 3y = 12 → 3y = 9x - 12 → y = 3x - 4.
B) Now comparing y = 3x - 4 by the general form of a straight line, we see that slope of this line is 3 and y-intercept is -4.
C) We have to find the equation of line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ).
As the lines are perpendicular, the slopes have the relation,
i.e.
i.e.
Now, using this slope and the point ( 3,5 ) , we will find the equation of the line using the formula,
i.e.
i.e.
i.e.
So, the line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ) is .
Step-by-step explanation:
