Equation in Slope-Intercept form?
I need help understanding how to work these types of problems out:
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of each equation.
2x + y = 5; (3, 1)
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of each equation.
x - 6y = 2; (2, 4)
- 1 decade agoFavorite Answer
slope-intercept form -> y=mx+b
2x+y = 5
y = -2x + 5
So, the slope of our line is -2x; therefore, a line parallel to this one MUST have the same slope (check on paper!). We know it passes through the point (3,1) where x = 3, and y =1
using point-slope formula:
y-1 = -2(x-3)
slope = 1/6
We know that the slope of the line we have times the slope of a perpendicular line we are trying to find will be = -1. You can verify this from your textbook or an online source. Let M be the slope of the perpendicular line we are trying to find:
1/6(m) = -1 from our identity above
m = -6 which is the slope of our perpendicular line
We know it passes through the point (2,4) so we use point-slope formula again:
- 1 decade ago
Find the slope of the given equation, then plug that into a new equation that should look like (in the case of your first problem)
y= -2x + b <y-intercept
Then find b, by graphing, mental work, or just plug in the coordinates into the new equation.
(3,1) 1 = -2(3) + b Solve for b (it should be 7)
For the second one you need to use the opposite reciprocal of the slope and do the same thing.
Opposite= negative of whatever it is referring to
Reciprocal= The number one divided by whatever it is referring to
The opposite reciprocal of that slope would be -6.
Math dominates, JONNy-G
- 1 decade ago
Do your own homework man!!