Writing Equations in Slope Intercept Form

Use the formula y = mx + bm= 5/4x = 8y = 5Now solve for bb =-5y = (5/4)*x -5

We know:[math]-6m+c=5[/math]And we know:[math]mx+c \ne -12+4x[/math]We can solve this like a normal equation:[math]x \ne \frac{-(12+c)}{m-4}[/math]But for any [math]m[/math] we enter we will get a vaild [math]x[/math], except for the case [math]m=4[/math]So we have the form[math]4x+c[/math]And from there we know:[math]-24+c=5[/math]we add [math]24[/math] to both sides and get:[math]c=29[/math]So our line has the form [math]4x+29[/math]And it it easy to see that it is paralell since [math]-12 \ne 29[/math].

To start, let’s look at the general setup of equations in slope-intercept form.(y-y1)=m(x-x1), with m being the slope, and x1 and y1 being the coordinates of the given point on the graph. Now, all you have to do is plug in the information where it belongs.The y coordinate replacing y1, the x coordinate replacing x1, and the slope replacing m.The equation of the line is y= -5, meaning the slope is zero. So for m, you would plug in zero.Equation: y-(-5)=0(x-(-5)y+5=0(x+5)Final: y+5=0

The equation for slope-intercept form is                             [math]y = mx =  + b[/math]where [math]x[/math]and [math]y[/math]are the variables, [math]m[/math]is the slope, and [math]b[/math]is the y-intercept.If                             [math]m = 9[/math] and [math]b =  - 5[/math]then the equation in slope intercept form would be:                            [math]y = 9x + \left( { - 5} \right)[/math]                            [math]y = 9x - 5[/math]Here Slope intercept form: y = mx + b are some example of how you deal with slope-intercept form. I think it will be worth while to take a look.

Slope-intercept is a specific form of linear equations. It has the following general structure. Drum roll ...y=mx+by,Here, m and b can be any two real numbers. For example, these are linear equations in slope-intercept form:y=2x+1yy=−3x+2.7yy=10−100xyOn the other hand, these linear equations are not in slope-intercept form:2x+3y=5y−3=2(x−1)Slope-intercept is the most prominent form of linear equations.For more information please watch the below video :

Slope intercept form requires two pieces of information; a slope, m, and the y-intercept, b. It is written y = mx + b.The slope is given by the line it is parallel to your desired line, because parallel lines have the same slope. The given line has a slope of 3, so your new line has a slope, or m of 3.To find b, plug in any point and the slope and isolate b.y = (3)x + b now plug in the point you have (-4,5)5 = (3)(-4) + b simplify5 = -12 + b add 12 to both sidesb = 17 Now you know the y-intercept is 17y = 3x + 17 Check 5 = (3)(-4) + 17 => 5 = -12 + 17 => 5 = 5

(3, 4), (-6, 2)∆y/∆x = (2–4)/(-6–3) subtract y2-y1 over x2-x1∆y/∆x = -2/-9∆y/∆x = 2/9 = slopeOr∆y/∆x = (4–2)/(3– -6) you can try it the other way, it will still come out the same!∆y/∆x = 2/9 = slopeNow use point-slope form to determine b or y intercept:y - y1 = m(x - x1) sub in (x,y) and use either set of coordinatesy - 4 = 2/9(x - 3) solvey - 4 = 2/9 x - 2(3)/9 work towards isolating yy - 4 + 4 = 2/9 x - 6/9 +4 yep, add 4 to both sides of the equationy + 0 = 2/9 x - 6/9 + 4(9)/9 it's beginning to go towards being in slope-intercept form. Finding a common dinominator so you can add -6/9 + 4y = 2/9 x + (-6 + 36)/9 solvey = 2/9 x + 30/9y = 2/9 x + 10/3y = mx + bSlope-intercept form!!m = 2/9b = 10/3 = 3 1/3

There are two steps to writing these equations.Find the Slope Fraction for the line.(This is the “m” in y=mx+b).Figure out how far up or down you have to move the line to match the two points.(This is the +b part of y=mx+b).Find the slope fraction from the line:There are two ways to find the slope from two points.The visual way is to graph each point and then count the number of squares up (rise), then the number of squares over (run) between the points.This makes the slope fraction [math]\frac{rise}{run}[/math]Graphing the two points in a.) gives me a rise of 3 and a run of 2. The slope fraction is 3/2.The other way to find the slope is with Arithmetic. You subtract one Y value from the other and one X value from the other. This makes the slope fraction [math]\frac{(Y_1-Y_2)}{(X_1-X_2)}[/math]Using arithmetic for the points in b.) gives me [math]\frac{(5–8)}{(-3 - (-6))}[/math]Doing the subtraction[math]\frac{(-3)}{(3)}[/math]and reducing the fraction gives me[math]\frac{(-1)}{(1)}[/math]Which reduces even further to -1. -1 is the “slope fraction” for the second set of points.Move the line up or down with +bAfter you know the slope fraction, the next part is to figure out the “b” part of y=mx+b. Here’s how.Visually:Take a piece of graph paper and graph the two points you are given.Now take the slope fraction you found before, and plug it into this equation. y=(slope fraction) * x and graph it.If your line and the two points line up perfectly, then you are done. The equation for the line is y=(slope fraction) * x. That is the case for your first set of points. The answer is [math]y=\frac{3}{2}x[/math]With many problems, the line and your two target points won’t line up. There will be a gap between them. You have to move your y=(slope fraction) * x line up or down to make them line up.To do this, count how far above or below the points your line is. If your line is below the points, add this number to your y=(slope fraction) * x equation. If your line is below the points, subtract the number from your y=(slope fraction) * x equation.This next part is very important. Once you have your y=(slope fraction) * x + (some number) equation, graph it and make sure your answer is correct. If it isn’t, keep playing with the line, moving it up or down, until you find the right offset.You can also find this move-up-or-down number with arithmetic. Here’s how.Take one of your points (x, y) and your slope fraction (slope fraction is really long to type. Let’s call this M instead of “slope fraction”) , and plug it in this equation.b = y - mx(If you look closely at this, you’ll see I just rearranged “y=mx+b” to make this.)Once you’ve figured out b, you can put it in the y=mx+b equation and have your answer.Here’s what this looks like for your problem b.)We know the slope fraction = m = -1.We know one of the points is (-3,5).Plugging that in to my b=y-mx equation looks like this.b = 5 - (-1)*-3.Simplifying…b= 5- 3b= 2… and now I can plug the slope fraction (m) and this value for b into y=mx+b.y=mx+by= (-1)x + 2y= -x + 2Last but not least, and most importantly, I want to check this answer to make sure it’s right. I can do this by graphing the equation to make sure the points line up, or by plugging in the known points to make sure they work in the equationFrom problem b, the points are(-3, 5)plugging this in to y=-x+2 gives 5=- (-3) +2.This simplifies to 5=5.5 is equal to 5, so this point checks out.(-6, 8)plugging this in to y=-x+2 gives 8=- (-6) +2.This simplifies to 8=88 is equal to 8, so this point checks out.Both points check, so y=-x+2 is the answer to question b.)HTH

Slop-intercept form is y = mx + b, where m is slope and b is the y-intercept.Good news! You already have the y intercept! It's 7.Now you just need the slope. You have two points (-6, 0) and (0, 7). Using the slope formula, we can find the slope, which is [math]\frac{7}{6}[/math], but I prefer to visualize things.What's the "rise" (the change in y?) What's the "run" (the change in x?)Now that we have both our slope and our y-intercept, we plug them in:[math]y= \frac{7}{6}x + 7[/math]

The 4 2 skills practice writing equations in slope intercept form is designed to help students understand and apply the concept of slope-intercept equations in their math studies. It provides structured exercises that enhance their ability to write and interpret these equations accurately.

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