Question

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A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation y = mx + b.
A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope of -0.5. The y-intercept of the line is ___________
.

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Answer 1

Answer: The y-intercept of the line is 6

Explanation:

The equation of the line in the form
`y = mx + b` is called "Slope-Intercept form", where "m" is the slope of the line and "b" is the y-intercept.

Knowing that the line passes through the point (10,1) and has a slope of -0.5, we can identify that:

`x=10\\y=1\\m=-0.5`

Then, we can substitute values into the equation
`y = mx + b` and solve for "b".

`1=(-0.5)(10)+b\\\\1=-5+b\\\\1+5=b\\\\b=6`

Therefore, the y-intercept of the line is 6 .

Answer 2

6

Explanation:

A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation
`y = mx + b`.

If a line has the slope of -0.5, then m=-0.5 and the equation of the line is

`y=-0.5x+b`

This line passes throughthe point (10,1), then the coordinates of this point satisfy the equation of the line:

`1=-0.5\cdot 10+b\\ \\1=-5+b\\ \\b=1+5\\ \\b=6`

and the equation of the line is

`y=-0.5x+6`

Since b=6, the y-intercept of the line is 6.