Write The Equation Y - 2 = 4 X 5 In Standard Form.

How can I write the standard form of the equation of the line through the given point with the given slope? Given through is (4,-2) and the given slope is -1.

I have very strong views on this type of question and I always encourage students to use LOGIC and NEVER to rely on any standard formulas.I think the most useful “standard form” of a line equation is y = mx + c where m is the gradient and c is the intercept on the y axis.The other “standard form” is not at all friendly or useful to me.It is ax + by + c = 0So your question says the gradient m = – 1 and it goes through (4, – 2)This is my logic…The equation must be y = – 1x + c and if it goes through (4, – 2) then we just substitute x = 4 and y = – 2 in order to find what c must be… here goes…–2 = –4 + cSo c = 2 and the equation is y = –x + 2____________________________________________________________

How can I write the standard form of the equation of the line through the given points? The given through are (-3,2) and (0,1).

y = mx + c is the standard equation for a line.Where,m is the gradient of the slopec is the intersection of the graph with the y-axisy is any y co-ordinate on the linex is any x co-ordinate on the lineTo find the gradient we use the formula: m= [math]\frac {y_2-y_1}{x_2-x_1}[/math]([math]-3,2[/math]) is ([math]x_1, y_1[/math]) and ([math]0,1[/math]) is ([math]x_2,y_2[/math])So the gradient= [math]\frac {1–2}{0–(-3)}[/math]= [math]\frac {-1}{3}[/math]therefore, m=[math]\frac {-1}{3}[/math]y = [math]\frac {-1}{3}x+c[/math][math](0,1)[/math] is when the line crosses the y-axis since there is a y value when x=oSo, the equation becomes y = [math]\frac {-1}{3}[/math] x + 1But for the sake of future questions, let’s use (-3,2)y=2 and x=-3[math]2 = \frac {-1}{3} × (-3) + c[/math]2 = 1 + cc = 2–1c=1Therefore, y = [math]\frac {-1}{3}[/math] x + 1

How can I write an equation in standard form given slope and y-intercept?

The standard form equation of a line is in the form [math]A•x + B•y = C [/math]Where [math]A: A \in \Bbb Z^+ [/math]and [math]B, C: B, C \in \Bbb Z [/math]Given slope [math](m) [/math]and y intercept [math]c [/math], the slope intercept form of the line can be written as:[math]y = m•x + c (1)[/math][math]A [/math]should be positive, thus writing the standard form from slope intercept form changes based on the sign of [math]m.[/math]If [math]m [/math] is positive.Rewrite (1)We get: [math]mx - y = -c [/math]Express [math]m [/math]and [math]c [/math]in the form of rational numbers. I.e know the form [math]\frac{i}{j} [/math]where [math]i, j: i, j \in \Bbb Z. [/math]Take the lcm [math]k[/math] of the denominators of [math]m [/math]and [math]c. [/math]Make [math]k [/math]the common denominator for the entire equation.Multiply through by [math]k. [/math]The resulting equation:[math]Ax + By = C [/math]is in standard form.If [math]m [/math]is negative.Rewrite (1)We get: [math]mx + y = c [/math]Express [math]m [/math]and [math]c [/math]in the form of rational numbers. I.e know the form [math]\frac{i}{j} [/math]where [math]i, j: i, j \in \Bbb Z. [/math]Take the lcm [math]k[/math] of the denominators of [math]m [/math]and [math]c. [/math]Make [math]k [/math]the common denominator for the entire equation.Multiply through by [math]k. [/math]The resulting equation:[math]Ax + By = C [/math]is in standard form.

Write the equation, in standard form, of the circle with radius 4 and center (-1, 0)?

The equation of a circle is as follows:[math](x-h)^2+(y-k)^2=r^2[/math]Here, [math](h,k)[/math] is the centre of the circle and [math]r[/math] is the radius.On comparing with [math](-1,0)[/math], we get,[math]h=-1[/math] and [math]k=0[/math] along with [math]r=4[/math].Substituting these values in the equation, we get,[math](x-(-1))^2+(y-0)^2=(4)^2[/math][math](x+1)^2+y^2=16[/math]This is the equation of the circle with centre [math](-1,0)[/math] and radius [math]4[/math] which can further be expressed as[math]x^2+2x+1+y^2=16[/math][math]x^2+y^2+2x-15=0[/math]Hope this helps! You can also get such questions solved and get the detailed solution within seconds using the Scholr app by just uploading a picture of the question and also get to be a part of an ever-growing community of students.