What line is perpendicular to the line 2x + 3y = 6 through (4, 1)? Explanation: The given equation is in standard form, so it must be converted to slope-intercept form: y = mx + b to discover the slope is –2/3. To be perpendicular the new slope must be 3/2 (opposite reciprocal of the old slope).
What is the slope of the line with the equation 2x 3y 6?
Rearrange – 2x + 3y – 6 = 0 into this form. Slope of the given equation is 23 and intercept on y axis is 2.
How do you find the equation of a perpendicular line?
Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = 1⁄2x + 6 . Rearranged, it is –x/2 + y = 6.
What is the y-intercept of the line with the equation − 2x 3y 6?
The y-intercept is simply y=2 .
What is the slope for 2x 3y =- 6?
Reorder −2 – 2 and 2×3 2 x 3 . Rewrite in slope-intercept form. Using the slope-intercept form, the slope is 23 .
What is the rule for perpendicular lines?
Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope. Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .
What is the equation of the line?
The general equation of a straight line is y = mx + c , where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
What is the slope and y-intercept of the line 2x 3y 6?
The slope is the number attached to x and the y-intercept is your ‘b’ term in the equation y=mx+b. So, the slope would equal 23 and the y-intercept would be −2 .
What is the slope of 2x y 6?
this is the y = mx + b form, where m is the slope. So your slope is 2 .
What is the slope of a line that is perpendicular to the line 2x 3y 5?
Explanation: Lines that are perpendicular will have negative reciprocal slopes . Meaning, if one line’s slope is m , then a perpendicular line will have a slope of −1m .
What are the intercepts of 2x 3y =- 6?
Given, [ – 2x + 3y = 6]. [ Rightarrow x = – 3]. Thus ‘x’ intercept is [ – 3] . [ Rightarrow y = 2].
What are the intercepts for 2x 3y 6?
For intercepts on y axis, put x=0 i.e. Hence, intercept on y axis is 2 .
What is the graph of 2x 3y 6?
We now have the equation of the line as 2x + 3y = 6. We can find the points and sketch the graph. Hence, the point is (0, 2). Hence, the point is (3, 0 ).
How do I find the slope of the line?
Using two of the points on the line, you can find the slope of the line by finding the rise and the run . The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .
Is the line perpendicular or parallel?
If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect . Their intersection forms a right, or 90-degree, angle.
How do you know if a line is parallel or perpendicular?
Answer: Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.
