Question

Type the correct answer in the box. Use numerals instead of words.
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:

6

Step-by-step 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.

Answer 2

Answer: The y-intercept of the line is 6

Step-by-step 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 .