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reinhard10158

Step-by-step explanation:

the general equation for a line is usually

y = ax + b

a is the slope (the inclination) of the line indicating how flat or steep (and up or down) the line goes. it is the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

and b is the y-intercept, the y value for x=0, the point, where the line intercepts the y-axis.

the origin is the point (0, 0).

that gives us the y-intercept (b) right away, as this is therefore clearly the point, where the line intercepts the y-axis. so, b = 0.

and going from (0, 0) to (-2, 10) we see

x changes by -2 (from 0 to -2).

y changes by +10 (from 0 to 10).

so, the slope is +10/-2 = -5.

and the line equation is

y = -5x

InLoveWithNature

[tex]\huge \text{Hello there! :)}[/tex]

Answer:

[tex]y=-5x[/tex]

Step-by-step explanation:

Given that the equation of a line passes through the origin and the point (-2,10), we can get the equation of the line below.

The slope-intercept form of the equation of the line is given as;

[tex]y=mx+b[/tex]

where m = slope and y = intercept

The formula for the slope is given as

[tex]\frac{y^{2-yx^{1} } }{x^{2-x^{1} }}[/tex]

The given points are the origin are (0,0) and (-2, 10)

[tex]m=\frac{10~-~0}{-2~-0} =\frac{10}{-2} =-5[/tex]

Now use the point-slope formula to solve for the equation of the line.

[tex](y-y^{1})=m(x-x^{1})[/tex]

For this situation, we are given the slope of -5 and (-2,10)

[tex]y-10=-5(x-(-2))[/tex]

[tex]y-10=5x-10[/tex]

[tex]Y+5x=+10-10[/tex]

[tex]y+5x=0[/tex]

[tex]y=-5x[/tex]

Therefore, the Answer is [tex]y=-5x[/tex]



[tex]\huge \text{Thanks for useing brainly!}[/tex]

[tex]\huge \text{Hope this helps!}[/tex]

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