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Alborosie
2 years ago
11

Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line

Mathematics
1 answer:
DedPeter [7]2 years ago
7 0

Answer:

An equation in standard form for the line is:

\frac{5}{2}x-y=-4

Step-by-step explanation:

Given the points

  • (-2, -1) and (0, 4)

The slope between two points

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)

m=\frac{4-\left(-1\right)}{0-\left(-2\right)}

m=\frac{5}{2}

Writing the equation in point-slope form

As the point-slope form of the line equation is defined by

y-y_1=m\left(x-x_1\right)

Putting the point (-2, -1) and the slope m=1 in the line equation

y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)

y+1=\frac{5}{2}\left(x+2\right)

y=\frac{5}{2}x+4

Writing the equation in the standard form form

As we know that the equation in the standard form is

Ax+By=C

where x and y are variables and A, B and C are constants

so

y=\frac{5}{2}x+4

\frac{5}{2}x-y=-4

Therefore, an equation in standard form for the line is:

\frac{5}{2}x-y=-4

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