Point-Slope Form #4: Fill & Download for Free

Why not open your text book and look for it yourself? Anyway I posted it here for you.

To solve any maths thing, you find the set of numbers that make the equations true.That is what “solve” means, in maths.The question is about the forms of the equation for a straight line.The analytic equation of a line is y = mx+c … m is the slope and c is the y-intercept (just the value of y when x = 0).If you know the slope and the y-intercept, this is handy.But what if you know the slope but, instead of the y-intercept, you know some other point (p,q) that is on the line?You can find the analytic form by subbing the point in:[math]q = mp [/math][math][/math][math]+ c[/math][This must be true because we just said that (p,q) is a point on the line y = mx + c.]…so, we can solve for c:[math]c = q-mp[/math]And the equation becomes:[math]y = mx [/math][math][/math][math]+ q - mp[/math]Which is usually written:[math](y-q) = m(x-p)[/math]… which mathematicians find more appealing.Note: the analytic equation is this one, if p = 0 and q = c. Try it.Mathematicians love standard form though… the “standard form” for a line is usually something like: [math]Ax [/math][math][/math][math]+ By [/math][math][/math][math]+ C = [/math][math][/math][math] 0[/math]We can put that into analytic form:[math]y = -(A/B)x - (C/B) = mx [/math][math][/math][math]+ c[/math], so [math]c = -C/B[/math] and [math]m = -A/B[/math]And point-slope form follows.[math](y-q) = -(A/B)(x-p)[/math]Bottom line is that you only need to remember one of them, and what the others are… and use algebra to convert between them. Just remember the one you are most comfy with.In practice, nobody uses all of them, we just use the one that we are used to.

Yes, if you are given any two points, an equation can be produced or defined.The point-slope form of a linear equation is defined as [math]y-y_1=m(x-x_1)[/math].Therefore, a point-slope form of a linear equation can be found when you either have two given points, or the slope of the line and one point.In this case, you are given two points — (-5, -2), (4, -3).Since you have two points, you must first find the slope. The formula for the slope of a line given two points is: [math]m=\frac{y_2-y_1}{x_2-x_1}[/math].In this example, [math]x_1=-5, x_2=4, y_1=-2, x_2=-3.[/math][math]m=\frac{(-3)-(-2)}{(4)-(-5)} => \frac{-1}{9}.[/math]Therefore, [math]m=\frac{-1}{9}[/math]Now that you know the slope (m) is equal to [math]\frac{-1}{9}[/math], you can figure out the point-slope form of the equation.Substitute the corresponding values into the point-slope form “formula.”[math]y-(-2)=\frac{-1}{9}(x-(-5)) => y+2=\frac{-1}{9}(x+5).[/math]Therefore, the point-slope form of the equation given the points (-5, -2), (4, -3) is:[math]y+2=\frac{-1}{9}(x+5).[/math]Hope I helped!