Wrote An Equation Of The Line In Slope Intercept Form

Question

forgive me for being stupid, but I seriously have no idea how to solve this.. 

The question is: Write an equation of the line in slope intercept form that passes through the point and givem slope. 

(0,-9) and slope =4

Answer 1

Hi Julia, there are three forms of the line equation, the standard form, the slope-intercept form, and the point-slope form. They are all basically the same.

 

Standard form: Ax + By = C

 

Slope-intercept form: y = mx + b

 

Point-slope form: y - y₁ = m * (x - x₁)

 

Which one you start with depends on what you know. In this problem, you have a point and a slope. Therefore, you would start with the point-slope form and then convert it to the slope-intercept form.

 

Point-slope form:

 

m = 4

 

x₁ = 0

 

y₁ = -9

 

Substitute for into the point-slope form:

 

y - (-9) = 4 * (x - 0)

 

y + 9 = 4x

 

Convert to slope-intercept form:

 

To get y + 9 = 4x into the slope-intercept form, subtract 9 from both sides:

 

y = 4x - 9

 

We could have used the information give to write the slope-intercept form directly. The point given, (0, -9) is the point where the line crosses the y-axis. Therefore, we know what b is in the slop-intercept form. It is -9. The slope, m is given. Therefore, we can use 4 as the slope.

 

Simple substitution would be: y = 4x -9.

 

Keep in mind this is a special case. If the given point has any value for x other than zero, you cannot find the line by simple substitution.

 

Questions?

Answer 2

y = mx + b

y = 4x + b

 

-9 = 4(0) + b

-9 = b

 

y = 4x - 9