What is the equation in slope intercept form that passes through the point (3,9) and has a slope of -5?

2 Answers
Dec 9, 2017

y=-5x+24

Explanation:

Given:

Point: (3,9)

Slope: -5

First determine the point-slope form , then solve for y to get the slope-intercept form.

Point-slope form:

y-y_1=m(x-x_1),

where:

m is the slope, and (x_1,y_1) is a point on the line.

Plug in the known values.

y-9=-5(x-3) larr Point-slope form

Slope-intercept form:

y=mx+b,

where:

m is the slope and b is the y-intercept.

Solve for y.

Expand the right-hand side.

y-9=-5x+15

Add 9 to both sides.

y=-5x+15+9

Simplify.

y=-5x+24 larr Slope-intercept form

Dec 9, 2017

Since the slope-intercept form is y = mx + b and we do not know the y-intercept (b), substitute what is known (the slope and the point's coordinates), solve for b, then obtain y = -5x + 24.

Explanation:

The slope-intercept form is y = mx + b. First, we write down what we already know:
The slope is m = -5,
And there's a point (3, 9).

What we do not know is the y-intercept, b.
Since every point on the line must obey the equation, we could substitute the x and y values that we already have:
y = mx + b becomes 9 = (-5) * 3 + b

And then solve algebraically:
9 = (-5) * 3 + b
Multiply:
9 = (-15) + b
Add both sides by 15:
24 = b
So now we know that the y-intercept is 24.

Therefore, the slope-intercept form for this line is:
y = -5x + 24