Question

What is the equation of the line in slope intercept form of slope 8 and point (0,-6)

Answer 1

Answer:

y = 8x - 6

Step-by-step explanation:

Point-slope form is y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line and m is a slope.

Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.

Normally, when you are given a slope and a point on the line and asked to find the equation of the line in slope-intercept form, you would first write a line in point-slope form and simplify it into slope-intercept form (there is an easier way to do it). You would do it like this:

y - (-6) = 8(x - 0)

Simplify

y + 6 = 8x

Subtract 6 from both sides.

y = 8x - 6

You can do this here, but if you look at the point carefully, you can see that the point we are given lies on the y-axis, and is therefore the y-intercept of the line. So we can put it into slope-intercept form with 8 as the slope and -6 as the y-intercept:

y = 8x + (-6)

Simplify

y = 8x - 6

As you can see, both ways of solving this problem yield the same answer, but the second way that I showed is, in mu opinion, easier.

I hope you find my answer helpful.