What is the slope intercept form of the equation?

Question

Y=-3/4x and passes through (4,-1)

Answer 1

The slope intercept form is y=mx+b but in order to achieve this form using the given information we will have to apply the following steps.

1. Are you asking for the equation of a line parallel or perpendicular to the line y=-3/4x?
2. if parallel: the slopes will always be the same for both lines so we will use the slope of y=-3/4x which is m=-3/4.
3. if perpendicular: the slopes are always negated reciprocals so we will take the slope of the line y=-3/4x and change the sign then flip the fraction. The slope of your new line would then become m=4/3.
4. take the slop and the point that the line will go through and plug it into the point-slope form.
5. y-y₁=m(x-x₁) :point-slope form let m=slope and (x₁,y₁) =(4,-1)
6. if parallel: m=-3/4
7. y-(-1) = -3/4(x-4)
8. y+1=-3/4x+3 simplify and distribute
9. y+1-1=-3/4+3-1 subtract 1 from both sides
10. y=-3/4+2 final answer in slope-intercept form
11. if perpendicular: m=4/3
12. y-(-1)=4/3(x-4)
13. y+1=4/3x-16/3 simplify and distribute
14. y+1-1=4/3x+16/3-1 subtract 1 from both sides
15. to subtract fractions with unlike denominators we find the common denominator and then we can combine
16. 16/3 -1 will then become 16/3-3/3 =13/3
17. y=4/3x+13/3 final answer in slope-intercept form

So your final asnwer would depend on whether the question is looking for the line parallel to or perpendicular to the line y=-3/4x.