Question

What is the equation of the line?

Answer 1

`\displaystyle y = -2x + 5`

Explanation:

From the y-intercept of
`\displaystyle [0, 5],`travel five units south over two units east. Doing so will get you to the endpoint of
`\displaystyle [1, 3],`which tells you that the rate of change is
`\displaystyle -2.`Therefore, your equation, in Slope-Intercept Form, is
`\displaystyle y = -2x + 5.`

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Answer 2

`\sf y=-2x+5`

Explanation:

Choose 2 points on the line:

Let
`\sf (x_1,y_1)=(0,5)`

Let
`\sf (x_2,y_2)=(4,-3)`

Substitute these points into the slope formula to find the slope (m):

`\sf slope \ (m)=(y_2-y_1)/(x_2-x_1)=(-3-5)/(4-0)=-2`

Substitute point (0, 5) and the slope (m) into the point-slope form of a linear equation:
`\sf y-y_1=m(x-x_1)`

`\sf \implies y-5=-2(x-0)`

`\sf \implies y=-2x+5`