Write an equation in slope-intercept form of the line that passes through (2,2) and has a y-intercept of 7?
Slope intercept equation is y=mx+b. If it says you have a y-intercept of 7, the 7 replaces the b because the b is "y-intercept". So now you have y=mx+7. The point (2,2) refers to x and y. So you plug in 2 and 2 for x and y in the equation. 2=m2+7. To solve for m you have to isolate it, so you subtract seven from each side (-5=m2) and then you divide each side by 2 (-5/2=m). Now you have the information for your equation. . .m=-5/2 and b=7! y= -5/2x+7 That's how you do the problems with the example above. There's another kind of question they might ask and that is "Write an equation with the given points - (2,-4) and (4,1). Now what you do here is put those numbers in Point Slope form. And that form is (Y sub 2 - Y sub 1) divided by (X sub 2 - X sub 1). If you plug in those numbers the Y sub and X sub 2's are really the SECOND numbers in the coordinates. . .Y sub 2 is 1 and Y sub 1 is -4. X sub 2 is 4 and and X sub 1 is 2. That equation if you solve it right will give you the slope of the equation. The slope of this equation would be 5/2. Then you plug that in to y=mx+b...y=5/2x+b. To find the X and Y values, use the coordinates of the first ordered pair (2,-4) and plug those in. Then solve for b.
Which equation describes a line with a slope of -2/3 and a y-intercept of 1/2?
y = mx + b The line has a slope of -2/3 and a y-intercept of 1/2. y= (-2/3)x + 1/2 ---> what they did here is they multiplied the whole equation by the common multiple of 6 ( 3 and 2) to get rid of the fractions. 6 [y = (-2/3)x + 1/2] 6y = -4x + 3 6y + 4x = 3
Write the equation of the line given the slope and the y-intercept.?
first link (below) discusses, describes and provides examples for Straight-Line Equations: Slope-Intercept Form I think the most useful form of straight-line equations is the "slope-intercept" form: y = mx + b This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept. (For a review of how this equation is used for graphing, look at slope and graphing.) I like slope-intercept form the best. It is in the form "y=", which makes it easiest to plug into, either for graphing or doing word problems. Just plug in your x-value; the equation is already solved for y. Also, this is the only format you can plug into your (nowadays obligatory) graphing calculator; you have to have a "y=" format to use a graphing utility. But the best part about the slope-intercept form is that you can read off the slope and the intercept right from the equation. This is great for graphing, and can be quite useful for word problems. Copyright © Elizabeth Stapel 2000-2011 All as a last resort, enter the criteria at the web second page Find the Equation of a Line Given That You Know Its Slope and Y-Intercept
Write an equation in slope intercept form help?!?
1)Write an equation in slope intercept form for the line that passes trough (4,5) and is perpendicular to the -2x - 8y = 16 . First, we have to solve -2x - 8y = 16 for y. -2x-8y=16 -8y=2x+16 Add 2x on both sides. y=-2/8x+16/-8 Isolate the variable, y by dividing -8 on both sides. y=(-2/8x)/(2/2)+-2 Simplify the fraction, -2/8 by dividing 2 on both sides. y=-1/4x-2 Perpendicular lines are negative reciprocals of each other. The line, -2x - 8y = 16 has the slope of -1/4. So the line perpendicular to it must have the slope of 3. Now the x and y values of the point(4,5) and the slope will be plugged into the slope intercept form, y=mx+b. This is done to find the y-intercept. x ,y (4,5) y=mx+b 5=3(4)+b 5=12+b Subtract 12 on both sides. -7=b Therefore, an equation in slope intercept form for the line that passes trough (4,5) and is perpendicular to the -2x - 8y = 16 is y=3x-7. 2)Write an equation in slope intercept form that describes the line that passes through (-3,1) and is parallel to y= 4x +1 Parallel lines have the same slope. The line y= 4x +1 has the slope 4, so the line parallel to it must have the slope of 4. Now the x and y values of the point(-3,1) and the slope will be plugged into the slope intercept form, y=mx+b. (-3,1) x ,y y=mx+b 1=4(-3)+b 1=-12+b Add 12 on both sides. 13=b Therefore, an equation in slope intercept form that describes the line that passes through (-3,1) and is parallel to y= 4x +1 is y=4x+13. Hope I Helped! :)
How do you write a equation of a line that has the same slope?
First we'll have to find the slope of line 2x - 5y = 12 , 2x - 5y = 12 => 5y = 2x - 12 => y = (2/5)x - 12/5 Compare this with the equation of the straight line y = mx + b, where 'm' represents slope and 'b' represents y-intercept we get, m = 2/5 ......................................... Now find the y-intercept of 4y + 24 = 5x 4y +24 = 5x => 4y = 5x - 24 => y = (5/4)x - 24/4 => y = (5/4)x - 6 Again compare this with the equation of a straight line, y = mx+b we get, b = -6 ......................................... Now put the value of slope 'm' and y-intercept 'b' from above in y = mx + b, we get, y = (2/5)x - 6 ................ (ANSWER) ......................................... Or we can further simplify he above equation as : Multiply both LHS and RHS by 5, we get 5y = 2x - 30 or 2x - 5y - 30 = 0 or 5y - 2x + 30 = 0 ( Both are similar, we can write it in both ways, one and the same thing) --------------------------------------... Hence the equation of the required line is 2x - 5y -30 = 0 ..... (ANSWER)
I have the slope -4, and the y-intercept 5. I need to make a slope-y-intercept equation for this. I need help.
What does a slope of -4 mean? A slope of -4 means that every time we increase x by 1 y decreases by 4 so it is sloping from left to right. You can get some graphing paper and plot out the points to visually understand this. Starting at the y-intercept plot x=0 and y=5 We know this is true because the y-intercept is equal to 5. When x = 0 (the y-intercept) y = 5. If we increase x to 1 we know the slope is -4 therefore y = 5-4=1. How do we turn all this information into an equation? The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.
Find the slope and y-intercept of the following line.... 3/2x+y=-5. please help me im totally lost!? Thanx?
Quite easy in fact. The basic formula for slop-intercept form is: y= mx + b where m is the slope and b is the y-intercept so basically if you have 3/2x +y = -5 then: 3/2x +5 = -y -3/2x -5 = y and if you look at the original slope-intercept form: -3/2 is the slope -5 is the y-intercept