Help please 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 if -0,5. The y-intercept of the line is _

y = -0.5x +6

Step-by-step explanation:

There are lots of different methods to do these types of questions, but this is the way i like to do it.

Coordinate (x1, y1) : (10, 1) and Gradient (m): -0.5

Start with this generic equation:

y- y1 = m(x-x1)

Substitute in the values they have given you:

y - 1 = -0.5(x-10)

This becomes:

y - 1 = -0.5x +5

Keep solving by moving the 10 over to the other side:

y = -0.5x +5 +1

y = -0.5x +6

An easy way to double check:

1) the coefficient of x is the slope. We got -0.5x, and the slope is -0.5, so that's correct.

2) Substitute x=10 into the equation, and we get 1, which is the exact coordinate that they gave us. This is also right.

Now that we've found the actual equation of the graph, we can easily find the y-intercept:

In the case of linear equations with structure y=mx +b, b is always the y-intercept.

so, since y = -0.5x +6, the y-intercept is 6. You can also find it by graphing or by letting x= 0. Either way, you will still get 6.  

Hope this helped : )

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