hi, im in the 9th grade and i need help I need help with my math. the following questions are?
we are learning parallel lines and perpendicular lines. think you can help me?
e) parallel to y=0 and passes through (1,2)
f) perpendicular to x=-1 and passes through (3,5)
g) slope is undefined and passes through (3,9)
h) 0 slope and passes through (5,6)
i) parallel to y= 3/4x +4 and same y-intercept as y=x-3/4
j) parallel to 2x-3=-1 and passes through (0,-3)
please, if you have the answers, explain how you got them and show me. please and thank you
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e) parallel to y=0 and passes through (1,2)
Ans: -
The line y=0 refers to the x-axis (y co-ordinate = 0)
Any line parallel to this will have its equation as y=c (where c is a constant.)
If it passes through (1,2) (y- co-ordinate =2), the equation should be y=2.
Of course! I'd be happy to help you with your math questions on parallel and perpendicular lines. Let's go through each question one by one:
e) To find a line parallel to y=0, we know that its slope should also be 0, as all parallel lines have the same slope. The equation of a line with a slope of 0 is y = b, where b is the y-intercept. Since the line passes through the point (1,2), we can substitute these values into the equation to solve for b:
2 = b. Therefore, the equation of the line is y = 2.
f) For a line perpendicular to x = -1, we need to find its slope. Since x is equal to -1 for all points on the line, the line is vertical and has an undefined slope. However, we can still determine its equation using the point (3,5) it passes through. The equation will be x = 3.
g) A line with an undefined slope is a vertical line. Since it passes through the point (3,9), we can say that x = 3 is the equation of the line, similar to the previous question.
h) A line with a slope of 0 is a horizontal line. The equation of such a line is y = b, where b is the y-intercept. Given that the line passes through the point (5,6), we can substitute these values into the equation to find b: 6 = b. Hence, the equation is y = 6.
i) To find a line parallel to y = 3/4x + 4, we know it should have the same slope of 3/4. Since both lines should have the same y-intercept, we can set the unknown line equal to y = mx + b and use the y-intercept of the given line, which is -3/4. Therefore, the equation of our parallel line is y = 3/4x - 3/4.
j) To find a line parallel to 2x - 3 = -1, we first need to rewrite the equation in slope-intercept form, y = mx + b. Solving for y, we get y = 2x + 2. As the new line should be parallel, it will have the same slope (2), but it needs to pass through the point (0, -3). By substituting these values into the equation y = mx + b, we can solve for b:
-3 = 2(0) + b. This simplifies to -3 = b. Thus, the equation of the line is y = 2x - 3.
These are the answers and explanations for each question. If you have any further questions or need more clarification, feel free to ask!