Use the following lines to answer the question.
line g: y=−45x+75
line h: y=54x+34
Is line g perpendicular to line h? Why or why not?
Yes, because the slopes of lines g and h are opposite and the y-intercepts are different.
Yes, because the slopes of lines g and h are opposite and reciprocal.
No, because the y-intercepts of lines g and h are different.
No, because the slopes of lines g and h have different signs.
Perpendicular slopes are negative reciporcals (that means if you multiply then together the answer is -1)
for example 2 slopes that belong to perpendicular lines are -3 and 1/3
because they multiply to get -1 , thus they cross at 90 degrees and are thus perpendicular.
Check the slopes (they are what is connected to x)
Wait im confused . how do i multiply them to get -1
Multiply the numerators (the tops of the fractions) together, and then multiply the denominators (the bottoms of the fractions) together and then simplify.
To determine if two lines are perpendicular, we need to examine the slopes of the lines.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
For line g: y = -45x + 75, the slope (m) is -45, and the y-intercept (b) is 75.
For line h: y = 54x + 34, the slope (m) is 54, and the y-intercept (b) is 34.
To determine if the lines are perpendicular, we need to check if the slopes are opposite and reciprocal.
In this case, the slopes of lines g and h are indeed opposite in sign (-45 and 54) and reciprocal (their product is -1), satisfying the condition for perpendicularity.
Therefore, the correct answer is: Yes, because the slopes of lines g and h are opposite and reciprocal.