Pls help me due Tuesday
1 answer:
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Answer:
see attached
Step-by-step explanation:
I find it convenient to let a graphing calculator draw the graph (attached).
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If you're drawing the graph by hand, there are a couple of strategies that can be useful.
The first equation is almost in slope-intercept form. Dividing it by 2 will put it in that form:
y = 2x -4
This tells you that the y-intercept, (0, -4) is a point on the graph, as is the point that is up 2 and right 1 from there: (1, -2). A line through those points completes the graph.
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The second equation is in standard form, so the x- and y-intercepts are easily found. One way to do that is to divide by the constant on the right to get ...
x/2 +y/3 = 1
The denominators of the x-term and the y-term are the x-intercept and the y-intercept, respectively. If that is too mind-bending, you can simply set x=0 to find the y-intercept:
0 +2y = 6
y = 6/2 = 3
and set y=0 to find the x-intercept
3x +0 = 6
x = 6/3 = 2
Plot the intercepts and draw the line through them for the graph of this equation.
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Here, we have suggested graphing strategies that don't involve a lot of manipulation of the equations. The idea is to get there as quickly as possible with a minimum of mistakes.
Answer:
The product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given the lines
y = 2/3 x -3 --- Line 1
y = -3/2x +2 --- Line 2
<u>The slope of line 1</u>
y = 2/3 x -3 --- Line 1
By comparing with the slope-intercept form of the line equation
The slope of line 1 is: m₁ = 2/3
<u>The slope of line 2</u>
y = -3/2x +2 --- Line 2
By comparing with the slope-intercept y = mx+b form of the line equation
The slope of line 2 is: m₂ = -3/2
We know that when two lines are perpendicular, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = (2/3)(-3/2 )
m₁ × m₂ = -1
Thus, the product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.